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No, the complete graph of 5 vertices is non planar. because we cant make any such complete graph which draw without cross over the edges . if there exist any crossing with respect to edges then the graph is non planar.Note:- a graph which contain minimum one edge from one vertex to another is called as complete graph...
false
yes
A cube is bipartite platonic graph. You can represent it as platonic by drawing one square inside another and connecting respective edges. Start from any vertex, name it A, color it black. Color the adjacent vertices red and name them B, C, D. Take one of the red vertices (i,e, B, C, D)and all adjacent vertices should be black... and so on. You will be able to get cube with no edges between two vertices of same color. This shows it should be bipartite as well as we used only two color to represent graph. Furthermore, put vertices of black and red color in two partitions and connect them with same edges as in the previous graph. Since, there is no edge between two vertices of same color this is bipartite graph as required.
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The automorphism group of a complete graph ( K_n ) (where ( n ) is the number of vertices) is the symmetric group ( S_n ). This is because any permutation of the vertices of ( K_n ) results in an isomorphic graph, as all vertices are equivalent in a complete graph. Therefore, the automorphism group consists of all possible ways to rearrange the vertices, corresponding to the ( n! ) permutations of the ( n ) vertices.
No, the complete graph of 5 vertices is non planar. because we cant make any such complete graph which draw without cross over the edges . if there exist any crossing with respect to edges then the graph is non planar.Note:- a graph which contain minimum one edge from one vertex to another is called as complete graph...
In a complete graph with ( n ) vertices, the number of distinct Hamiltonian circuits, not counting reversals, is given by ( \frac{(n-1)!}{2} ). For a complete graph with 7 vertices, this calculation is ( \frac{(7-1)!}{2} = \frac{6!}{2} = \frac{720}{2} = 360 ). Therefore, there are 360 distinct Hamiltonian circuits in a complete graph with 7 vertices when not considering reversals.
A complete graph is a type of graph in which every pair of distinct vertices is connected by a unique edge. In a complete graph with ( n ) vertices, denoted as ( K_n ), there are exactly ( \frac{n(n-1)}{2} ) edges. This means that every vertex is adjacent to every other vertex, resulting in a highly interconnected structure. Complete graphs are often used in graph theory to illustrate maximum connectivity among a set of points.
The term "cyclic graph" is not well-defined. If you mean a graph that is not acyclic, then the answer is 3. That would be the union of a complete graph on 3 vertices and any number of isolated vertices. If you mean a graph that is (isomorphic to) a cycle, then the answer is n. If you are really asking the maximum number of edges, then that would be the triangle numbers such as n (n-1) /2.
one vertex: 3 two vertices: 6 three vertices: 8 total 17
A star graph, call it S_k is a complete bipartite graph with one vertex in the center and k vertices around the leaves. To be a tree a graph on n vertices must be connected and have n-1 edges. We could also say it is connected and has no cycles. Now a star graph, say S_4 has 3 edges and 4 vertices and is clearly connected. It is a tree. This would be true for any S_k since they all have k vertices and k-1 edges. And Now think of K_1,k as a complete bipartite graph. We have one internal vertex and k vertices around the leaves. This gives us k+1 vertices and k edges total so it is a tree. So one way is clear. Now we would need to show that any bipartite graph other than S_1,k cannot be a tree. If we look at K_2,k which is a bipartite graph with 2 vertices on one side and k on the other,can this be a tree?
In an undirected graph, an edge is an unordered pair of vertices. In a directed graph, an edge is an ordered pair of vertices. The ordering of the vertices implies a direction to the edge, that is that it is traversable in one direction only.
If all the vertices and edges of a graph A are in graph B then graph A is a sub graph of B.
To find the number of vertices in an octagonal pyramid using a graph, you can represent the pyramid as a 3D shape with vertices, edges, and faces. An octagonal pyramid has 8 vertices, one at the top (apex) and 8 at the base. You can also draw a graph with each vertex representing a corner of the pyramid and each edge representing a line connecting two vertices. By counting the number of vertices in the graph representation, you can determine that an octagonal pyramid has a total of 9 vertices.
No of spanning trees in a complete graph Kn is given by n^(n-2) so for 5 labelled vertices no of spanning trees 125
Let G be a complete graph with n vertices. Consider the case where n=2. With only 2 vertices it is clear that there will only be one edge. Now add one more vertex to get n = 3. We must now add edges between the two old vertices and the new one for a total of 3 vertices. We see that adding a vertex to a graph with n vertices gives us n more edges. We get the following sequence Edges on a graph with n vertices: 0+1+2+3+4+5+...+n-1. Adding this to itself and dividing by two yields the following formula for the number of edges on a complete graph with n vertices: n(n-1)/2.