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Is the complete graph on 5 vertices planar?
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...
A digraph is a graph with exactly two vertices. true or false?
false
Is every simple graph on n vertices is isomorphic to a subgraph on kn?
yes
Which platonic graph is Bipartite?
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.
What is the minimum number of vertices of 3-regular graph with girth 6?
-3
Is the complete graph on 5 vertices planar?
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...
How many minimum edges in a Cyclic graph with n vertices?
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.
How many subgraphs with at least one vertex does a complete graph of 3 vertices k3 have?
one vertex: 3 two vertices: 6 three vertices: 8 total 17
Show that the star graph is the only bipartiate graph which is a tree?
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?
Difference between a directed graph and an undirected graph in a computer program?
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.
What is subgraph in given graph?
If all the vertices and edges of a graph A are in graph B then graph A is a sub graph of B.
How can i use a graph to find the number of vertices in a octagonal pyramid?
The number of vertices in an octagonal pyramid is 9, irrespective of any graph.
How many spanning trees can be drawn with 5 labeled 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
What is the maximum number of distinct edges in an undirected graph with N vertices?
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.
What is a drawing graph?
A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. In the abstract, all that matters is which pairs of vertices are connected by edges.
What is an adjacency matrix?
An adjacency matrix is a matrix showing which vertices of a graph are adjacent to which other vertices.
What is the total number of spanning tree that can be drawn using five labeled vertices?
125 according to Cayley's formula for counting spanning trees. For a complete graph Kn, t(kn) = nn-2 where n is the number of vertices.
