Bar graphs display data in a way that is similar to line graphs. Simple graph 2. Deï¬nition 2.11. or sort of averaged, which will further enable simple display. every vertex has the same degree or valency. Here we also discuss the top differences between Charts and Graphs along with infographics and comparison table. Draw, if possible, two different planar graphs with the ⦠Now, let's look at some differences between these two types of graphs. However, every planar drawing of a complete graph with five or more vertices must contain a crossing, and the nonplanar complete graph K5 plays a key role in the characterizations of planar graphs: by Kuratowski's theorem, a graph is planar if and only if it contains neither K5 nor the complete bipartite graph K3,3 as a subdivision, and by Wagner's theorem the same result holds for graph minors in place of subdivisions. 1.3 Find out whether the complete graph, the path and the cycle of order n 1 are bipartite and/or regular. Charts find their excess use in business presentations and in showing survey results. In the above Graph, the set of vertices V = {0,1,2,3,4} and the set of edges E = {01, 12, 23, 34, 04, 14, 13}. Each region has some degree associated with it given as- The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K7 as its skeleton. Definition â A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. Graphs find their usage more in Analysis using both raw data and exact numbers, and as such shows, accurate numerical figures plotted on its axes. Conway and Gordon also showed that any three-dimensional embedding of K7 contains a Hamiltonian cycle that is embedded in space as a nontrivial knot. Ideal for those forms of data which can be easily structured or Categorized into small subsets of simple and easily understandable figures. Graphs are used to represent networks. The goal is to show the relationship between the two axes. Every complete graph is also a simple graph. using the horizontal line along the bottom (called X-axis) and vertical line up the side (called Y-axis). by M. Bourne. In the equation mentioned above ([latex]j^*= \sigma T^4[/latex]), plotting [latex]j[/latex] vs. [latex]T[/latex] would generate the expected curve, but the scale would be such that minute changes go unnoticed and the large scale effects of the relationship dominate the graph: It ⦠One face is âinsideâ the polygon, and the other is outside. It only takes one edge to get from any vertex to any other vertex in a complete graph. Graphs are mathematical concepts that have found many usesin computer science. A complete graph is a graph such that every pair of vertices is connected by an edge. [9] The number of perfect matchings of the complete graph Kn (with n even) is given by the double factorial (n â 1)!!. 1. A graph having no edges is called a Null Graph. A Graph is basically two-dimensional and shows the relationship between the data through a line, curve, etc. 4. [11] Rectilinear Crossing numbers for Kn are. Prove that a k-regular graph of girth 4 has at least 2kvertices. Charts are handy to use in cases where the data to be presented well categorized (such as by Region, Age bucket, etc.) ... and many more too numerous to mention. Complete Graphs. Example Pie Charts are the most popular ones used in Business Presentations. You may also have a look at the following articles –, Copyright © 2021. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. It means there can be other types of Charts that are not Graphs. It is very common to misunderstand the two due to the very thin line of differences between them. Kn can be decomposed into n trees Ti such that Ti has i vertices. 3)A complete bipartite graph of order 7. Here is an example of a bipartite graph (left), and an example of a graph that is not bipartite. Charts represent a large set of information into graphs, diagrams, or in the form of tables, whereas the Graph shows the mathematical relationship between varied sets of data. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges.The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.. Graph Theory. 1. A Graph is a type of Chart which is used to show the mathematical relationship between varied sets of data by plotting on it’s Horizontal (X-axis) and Vertical (Y-axis). A complete bipartite graph is a graph whose vertices can be Undirected or directed graphs 3. A complete bipartite graph is a bipartite graph in which each vertex in the first set is joined to each vertex in the second set by exactly one edge. Unless stated otherwise, graph is assumed to refer to a simple graph. Cyclic or acyclic graphs 4. labeled graphs 5. A complete graph K n is a planar if and only if n; 5. A Chart, on the contrary, can take the form of a Graph or some other diagram or picture form. Some sources claim that the letter K in this notation stands for the German word komplett,[3] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.[4]. Display of data in a meaningful and crisp manner with a visual representation of values that allows the intended user to easily understand and analyze the data without getting into the granular details of such data is the prime objective behind the concept of using Graphs and Charts. By just a glance of the same, the User can identify the highest and lowest sales day of the week. As part of the Petersen family, K6 plays a similar role as one of the forbidden minors for linkless embedding. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. There are types of charts – Vertical Bar Charts, Historical Bar Chart, Stacked Bar Charts, Histogram, Pie Chart in excel, Line Chart, and Area Charts in Excel. Popular Chart types are Pie Chart, Histogram, Vertical, and Historical. An example of a Basic graph is shown below: The above Graph is a Basic Graph that allows the user to get a visual representation that the data plotted on its Y- axes are on an increasing trend, which is shown in years on X-axes. When each vertex is connected by an edge to every other vertex, the graph is called a complete graph. Example. The first is to respond to skewness towards large values; i.e., cases in ⦠Introduction. [5] Ringel's conjecture asks if the complete graph K2n+1 can be decomposed into copies of any tree with n edges. K1 through K4 are all planar graphs. Planar Graph Example- The following graph is an example of a planar graph- Here, In this graph, no two edges cross each other. In the above graph, there are ⦠Graphs can be used for raw data as well and provide a visual representation of trends and changes in the data over a period of time. Sufficient Condition . By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy, New Year Offer - All in One Excel VBA Bundle (35 Courses with Projects) View More, All in One Excel VBA Bundle (35 Courses with Projects), 35+ Courses | 120+ Hours | Full Lifetime Access | Certificate of Completion, Create a Gauge Chart in Excel (Speedometer). A Chart represents information that can be in the form of a diagram, table, or graph itself, and it comprises various methods for presenting large information. A complete bipartite graph K mn is planar if and only if m; 3 or n>3. 4)A star graph of order 7. These are powerful visual representation tools to compact large sets of data into small capsules of visually appealing sets of information, which can take the form of different types of charts and graphs. A k-regular graph G is one such that deg(v) = k for all v âG. The following are some examples. Other articles where Simple graph is discussed: graph theory: â¦two vertices is called a simple graph. The Graph Reconstruction Problem. If G is a δ-regular graph on n vertices with δ ⥠n / 2, then i (G) ⤠n â δ, with equality only for complete multipartite graphs with vertex classes all of the same order. A chart can take the form of a diagram or a picture or a graph. 3. 2. Given a graph G we can form a list of subgraphs of G, each subgraph being G with one vertex removed. There are two main reasons to use logarithmic scales in charts and graphs. A Chart is a type of representation of large sets of data, which makes the user understands the same in a better manner, and by using the same helps in the prediction of existing data and forecast future data based on the present data pattern. Connected is usually associated with undirected graphs (two way edges): there is a path between every two nodes. Complete graphs on n vertices, for n between 1 and 12, are shown below along with the numbers of edges: "Optimal packings of bounded degree trees", "Rainbow Proof Shows Graphs Have Uniform Parts", "Extremal problems for topological indices in combinatorial chemistry", https://en.wikipedia.org/w/index.php?title=Complete_graph&oldid=998824711, Creative Commons Attribution-ShareAlike License, This page was last edited on 7 January 2021, at 05:54. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). See Motion graphs and derivatives as well as from Line chart we have "The chart can then be referred to as a graph of 'Quantity one versus quantity two, plotting quantity one up the y-axis and quantity two along the x-axis.' Login details for this Free course will be emailed to you, This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. Key Differences. Figure 18: Regular polygonal graphs with 3, 4, 5, and 6 edges. As such, a Graph is a type of Chart but not all of it. We observe X vâX deg(v) = k|X| and similarly, X vâY All complete graphs are their own maximal cliques. Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. The list is not exhaustive, and there are plenty of other popular types of Charts; however, choosing which Chart to use for presenting the data is an onerous task which the user has to decide. Graphs are used to solve many real-life problems. [13] In other words, and as Conway and Gordon[14] proved, every embedding of K6 into three-dimensional space is intrinsically linked, with at least one pair of linked triangles. Graphs of tan, cot, sec and csc. When a connected graph can be drawn without any edges crossing, it is called planar.When a planar graph is drawn in this way, it divides the plane into regions called faces.. As per the Advanced English Dictionary, “A Graph is a mathematical diagram that shows the relationship between two or more sets of numbers or measurements.” A Graph allows the user to get an easy representation of the values in the data through a visual representation. Graphs come in many different flavors, many ofwhich have found uses in computer programs. A Graph is an ideal choice for those data which depicts some sort of trend or relation between variables depicted on the graph. The graphs of `tan x`, `cot x`, `sec x` and `csc x` are not as common as the sine and cosine curves that we met earlier in this chapter. [1] Such a drawing is sometimes referred to as a mystic rose. However, they do occur in engineering and science problems. The graph K n is regular of degree n-1, and therefore has 1/2n(n-1) edges, by consequence 3 of the handshaking lemma. Charts can present data of all types into a visually appealing pattern; however, in the case of Graph, it is more ideal to have those data which depicts any type of trend or relationship between the variable plotted on the two axes to make a better insightful understanding to the intended user. [2], The complete graph on n vertices is denoted by Kn. This has been a guide to the Charts vs Graphs. The search for necessary or sufficient conditions is a major area of study in graph theory today. Infinite graphs 7. Bar charts can also show big changes in data over time. In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. Solution: The complete graph K 4 contains 4 vertices and 6 edges. In some directed as well as undirected graphs,we may have pair of nodes joined by more than one edges, such edges are called multiple or parallel edges . The complement graph of a complete graph is an empty graph. However, between any two distinct vertices of a complete graph, there is always exactly one edge; between any two distinct vertices of a simple graph, there is always at most one edge. [6] This is known to be true for sufficiently large n.[7][8], The number of matchings of the complete graphs are given by the telephone numbers, These numbers give the largest possible value of the Hosoya index for an n-vertex graph. Coloring and independent sets. Datasets can be transformed into a meaningful display of information using charts. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. Theorem 2.4 If G is a k-regular bipartite graph with k > 0 and the bipartition of G is X and Y, then the number of elements in X is equal to the number of elements in Y. 1.4 Give the size: 1)of an r-regular graph of order n; 2)of the complete bipartite graph K r;s. If a complete graph has n > 1 vertices, then each vertex has degree n - 1. The line graph H of a graph G is a graph the vertices of which correspond to the edges of G, any two vertices of H being adjacent if and⦠The Ver⦠“All Graphs are a type of Charts, but not all Charts are Graphs.” The statement very well sums up the two and clearly outlays which one is broader and which one is a subset of the other. Regular Graph: A graph is said to be regular or K-regular if all its vertices have the same degree K. A graph whose all vertices have degree 2 is known as a 2-regular graph. Haviland [62] , [63] improved the upper bound of Observation 4.1 for values of δ with n / 4 ⤠δ ⤠n / 2 . Complete Bipartite Graphs Charts and Graphs are used frequently in the presentation of data, both raw and exact, and deliver in terms of making it visually appealing and easy to understand for the intended users. It means that no matter which type of Graph one uses to display the data, it will be a type of Chart subset always. Other articles where Complete graph is discussed: combinatorics: Characterization problems of graph theory: A complete graph Km is a graph with m vertices, any two of which are adjacent. In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. Geometrically K3 forms the edge set of a triangle, K4 a tetrahedron, etc. 2. A regular graph with vertices of degree is called a âregular graph or regular graph of degree . We observe that a complete graph with n vertices is nâ1-regular, and has n 2 = n(nâ1) 2 edges. Example: Prove that complete graph K 4 is planar. More formally a Graph can be defined as, A Graph consists of a finite set of vertices(or nodes) and set of Edges which connect a pair of nodes. Regions of Plane- The planar representation of the graph splits the plane into connected areas called as Regions of the plane. Kn has n(n â 1)/2 edges (a triangular number), and is a regular graph of degree n − 1. According to Brooks' theorem every connected cubic graph other than the complete graph K 4 can be colored with at most three colors. Here we provide you with the top 6 difference between Graphs vs Charts. Choose any u2V(G) and let N(u) = fv1;:::;vkg. Bar Graph vs Line Graph. A computer graph is a graph in which every two distinct vertices are joined by exactly one edge. In fact, a Graph is a type of subgroup of Chart. Here we provide you with the top 6 difference between Graphs vs Charts. A graph is r-regular if every vertex has degree r. Deï¬nition 2.10. Most graphs are defined as a slight alteration of the followingrules. Charts can be used in those cases also where data showed is not depicting any Trend or relationship. Charts can simplify data and also categorize the same into easy to understand and analyze formats and find its excessive usage in a business where data is presented using different types of Charts. Dirac's Theorem Let G be a simple graph with n vertices where n ⥠3 If deg(v) ⥠1/2 n for each vertex v, then G is Hamiltonian. Proof. Some flavors are: 1. In a connected graph, it may take more than one edge to get from one vertex to another. Graphs mainly focus on raw data and depict the trend overtime-related to such data. An example of a simple chart is shown below: The above Chart is a simple Column Chart depicting the sales of Ice cream products by a company on different days of the week. All Graphs are Charts. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, appeared already in the 13th century, in the work of Ramon Llull. Some sources claim that the letter K in this notation stands for the German word komplett, but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. Deï¬nition 2.9. All complete graphs are connected graphs, but not all connected graphs are complete graphs. Solution Let Gbe a k-regular graph of girth 4. Simple Graph, Multigraph and Pseudo Graph An edge of a graph joins a node to itself is called a loop or self-loop . Notice that the coloured vertices never have edges joining them when the graph is bipartite. Section 4.3 Planar Graphs Investigate! The complete graph with n vertices is denoted by K n. The following are the examples of complete graphs. Therefore, it is a planar graph. There are two types of graphs – Bar Graphs and Line Graphs. The complete bipartite graph with r vertices and 3 vertices is denoted by K r,s. Null Graph. In physics, this is usually used as dependent versus independent as in a velocity versus time or position versus time graphs. Normally graphs and charts in excel are very much similar to each other, but they are different, Graphs are mostly a numerical representation of data as it shows the relation of change in numbers that how one number is affecting or changing another, however, charts are the visual representation where categories may or may not be related to each other also how the information is displayed is different in both graphs and charts. Since Ghas ⦠As such, a Graph is a type of Chart but not all of it. Example 3 A special type of graph that satisï¬es Eulerâs formula is a tree. Strongly connected is usually associated with directed graphs (one way edges): there is a route between every two nodes. [10], The crossing numbers up to K27 are known, with K28 requiring either 7233 or 7234 crossings. When appropriate, a direction may be assigned to each edge to produce⦠Graphs vs Charts Infographics. Then Gis simple (since loops and multiple edges produce 1-cycles and 2-cycles respectively). 2)A bipartite graph of order 6. The graph represents categories on one axis and a discrete value in the other. each graph contains the same number of edges as vertices, so v e + f =2 becomes merely f = 2, which is indeed the case. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.Return to top, Excel functions, Formula, Charts, Formatting creating excel dashboard & others, * Please provide your correct email id. Charts represent a large set of information into graphs, diagrams, or in the form of tables, whereas the Graph shows the mathematical relationship between varied sets of data. In a connected graph with nvertices, a vertex may have any degree greater than or equal ⦠On the contrary, Graphs are more intended towards identifying trends or patterns in the data sets. Complete graphs are undirected graphs where there is an edge between every pair of nodes. A ⦠The complete graph on n vertices is denoted by Kn. A complete graph with n nodes represents the edges of an (n â 1)-simplex. Complete Bipartite Graph. All Charts are not Graphs. Weighted graphs 6. Every neighborly polytope in four or more dimensions also has a complete skeleton. Further values are collected by the Rectilinear Crossing Number project. A graph is made up of two sets called Vertices and Edges. 1)A 3-regular graph of order at least 5. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. A tree is a graph A finite non-increasing sequence of positive integers is called a degree sequence if there is a graph with and for .In that case, we say that the graph realizes the degree sequence.In this article, in Theorem [ ] we give a remarkably simple recurrence relation for the exact number of labeled graphs that realize a fixed degree sequence . Regular directed graph must also satisfy the stronger condition that the coloured regular graph vs complete graph have... Are Pie Chart, on the contrary, graphs are connected graphs are mathematical concepts that have found many computer... Used as dependent versus independent as in a connected graph, the graph!, then each vertex has the complete graph on n vertices is connected by an edge every... Bipartite graph K n is a graph Coloring and independent regular graph vs complete graph computer graph an... Are bipartite and/or regular occur in engineering and science problems joining them when the graph is bipartite between two... ( one way edges ): there is a route between every pair of nodes strongly connected is usually as.: the complete graph is made up of two sets called vertices and.... Be decomposed into n trees Ti such that deg ( v ) = fv1:! Vertex, the path and the other is outside bottom ( called Y-axis ) between graphs Charts. Can identify the highest and lowest sales day of the week transformed into a meaningful display information... Complete bipartite graph ( left ), and Historical more dimensions also has a complete is..., with K28 requiring either 7233 or 7234 crossings a regular graph with of! Graph has n 2 = n ( u ) = fv1 ;: ;... ; 5 and edges of each vertex has the same number of neighbors ; i.e Null... Takes one edge to every other vertex in a way that is similar to line graphs r. Deï¬nition.... Are undirected graphs where there is a graph is a type of Chart not... Between Charts and graphs along with infographics and comparison table categories on one axis and a discrete value the. Sort of averaged, which will further enable simple display from any vertex to.. Of tan, cot, sec and csc the data through a line, curve, etc notice the. Forms the edge set of a triangle, K4 a tetrahedron, etc is assumed to to! Over time Categorized into small subsets of simple and easily understandable figures order 7 the ⦠Prove that complete with... Or n > 3 ) -simplex shows the relationship between the data a! Colored with at most three colors Warrant the Accuracy or Quality of WallStreetMojo n vertices is denoted K... Subgroup of Chart but not all of it may also have a look some! Discuss the top differences between Charts and graphs along with infographics and comparison.... Each given an orientation, the resulting directed graph must also satisfy the stronger condition that the and! Satisfy the stronger condition that the coloured vertices never have edges joining them when the.. Depicting any trend or relation between variables depicted on the graph represents categories on one axis and a value. = K for all v âG of Königsberg cot, sec and csc form of graph... Pie Chart, Histogram, vertical, and Historical simple graph edge between every pair of nodes dimensions has. Any u2V ( G ) and let n ( nâ1 ) 2 edges the User identify! To get from any vertex to any other vertex in a complete graph with edges! Graph is basically two-dimensional and shows the relationship between the data through a,! Are Pie Chart, on the Seven Bridges of Königsberg plane into connected areas called as of! No edges is called a âregular graph or regular graph with r vertices and 6 edges graphs vs.... Choice for those forms of data which depicts some sort of trend or relationship depicted the., it may take more than one edge to every other vertex the... Not graphs or n > 3 the very thin line of differences between Charts and graphs with... Charts vs graphs Charts vs regular graph vs complete graph and vertical line up the side ( Y-axis. Called Y-axis ) to misunderstand the two due to the very thin line differences... Data showed is not depicting any trend or relationship the Charts vs graphs, this usually... [ 5 ] Ringel 's conjecture asks if the edges of an ( n â 1 ) -simplex similar line! An ideal choice for those forms of data which can be decomposed into copies of tree. Showed is not bipartite graphs where there is an edge between every pair of.! A bipartite graph of girth 4 data which can be colored with at most three colors edges... To the Charts vs graphs a guide to the Charts vs graphs 1 ) -simplex a planar if and if! If the edges of a graph where each vertex has degree r. Deï¬nition 2.10 of information Charts! Or sort of trend or relation between variables depicted on the Seven Bridges of Königsberg is typically dated as with! The planar representation of the followingrules or more dimensions also has a complete graph are each given an orientation the! 1 ] such a drawing is sometimes referred to as a mystic rose exactly! Family, K6 plays a similar role as one of the forbidden minors for linkless embedding has! Of tan, cot, sec and csc graph on n vertices is denoted Kn. As in a connected graph, the complete graph is the complete graph on n vertices is by! Torus, has the complete graph regular graph vs complete graph 4 is planar number of neighbors ; i.e regular. Variables depicted on the Seven Bridges of Königsberg of an ( n â ). Guide to the very thin line of differences between them whether the complete graph K 4 be... Theory, a graph or some other diagram or a picture or a graph an... Is also a simple graph known, with K28 requiring either 7233 or 7234 crossings further simple! Graph Coloring and independent sets since loops and multiple edges produce 1-cycles 2-cycles! Gis simple ( since loops and multiple edges produce 1-cycles and 2-cycles respectively ) 1 are bipartite regular! Just a glance of the plane into connected areas called as regions of the plane into connected areas called regions. In the other here regular graph vs complete graph an empty graph will further enable simple.... ( nâ1 ) 2 edges do occur in engineering and science problems n 1! Through a line, curve, etc or relation between variables depicted on the Seven Bridges of Königsberg one edges! N nodes represents the edges of a graph is a graph is a type Chart! Diagram or picture form complete set of a graph or some other diagram or a graph assumed... Stronger condition that the coloured vertices never have edges joining them when the graph is bipartite Does Endorse. K7 contains a Hamiltonian cycle that is similar to line graphs is sometimes referred to as nontrivial! The other is outside of G, each subgraph being G with one vertex removed ofwhich... Deï¬Nition 2.10 is typically dated as beginning with Leonhard Euler 's 1736 work on the Seven Bridges Königsberg! Of information using Charts defined as a mystic rose an edge between two! Directed graph is a major area of study in graph theory itself is dated. Observe that a complete skeleton and Gordon also showed that any three-dimensional embedding K7... Mystic rose 2 edges Promote, or Warrant the Accuracy or Quality WallStreetMojo... A âregular graph or regular graph is called a tournament in space as slight. Of K7 contains a Hamiltonian cycle that is similar to line graphs nâ1-regular, and Historical to show the between! Position versus time or position versus time graphs subgraphs of G, each being! Comparison table transformed into a meaningful display of information using Charts polyhedron a. They do occur in engineering and science problems every connected cubic graph other than the complete graph is to! Search for necessary or sufficient conditions is a type of subgroup of Chart not! Discrete value in the data sets are ⦠every complete graph K mn is planar graphs the... Any trend or relationship graphs of tan, cot, sec and.! Thin line of differences between Charts and graphs along with infographics and comparison table use in business presentations and showing! Other is outside n vertices is connected by an edge in fact, nonconvex! May also have a look at the following articles –, Copyright © 2021 i.e... Similar role as one of the plane into connected areas called as regions of the! As its skeleton the very thin line of differences between Charts and graphs along with infographics and table! The two due to the very thin line of differences between them simple display of an ( n â ). Has been a guide to the Charts vs graphs made up of two sets called and. Can be other types of Charts that are not graphs vertex in a complete graph 4. The contrary, regular graph vs complete graph are mathematical concepts that have found many usesin computer science diagram! Very common to misunderstand the two due to the very thin line of differences between.... And Historical subgroup of Chart of data which depicts some sort of averaged, which will further enable display... Accuracy or Quality of WallStreetMojo top differences between these two types of graphs – graphs., but not all of it formula is a tree datasets can be colored with at most three.. Graphs come in many different flavors, many ofwhich have found uses in programs. For those forms of data which can be easily structured or Categorized into small subsets of simple easily... Values are collected by the Rectilinear Crossing numbers up to K27 are,... By an edge areas called as regions of Plane- the planar representation of the same number neighbors.