Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.ans.148164 Previous Marked for Review Next
Question
Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.ans.148164 Previous Marked for Review Next
Solution
The number of spanning trees for a complete graph with n vertices is given by the formula n^(n-2). This is known as Cayley's formula.
So, for a complete graph G with 4 vertices, the number of spanning trees would be 4^(4-2) = 4^2 = 16.
Therefore, the graph G has 16 spanning trees.
Similar Questions
Consider a complete graph G with 3 vertices. The graph G has ____ spanning trees. Options 15 8 16 3
Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 3, 4, 5, 6, 7and 8. The maximum possible total weight that a minimum weight spanning tree of G can have is __.
A graph has r = 4 vertices and n = 5 edges. Then how many spanning trees can be drawn.a. 20 b. 22c. 18d. None of Them
Every graph has only one minimum spanning tree. State true or false.a)Trueb)False
Which of the following statements about spanning trees is false?AA spanning tree of a graph G is a subgraph that includes all vertices of GBA spanning tree can be a disconnected graphCA spanning tree has n−1 edges where n is the number of vertices in the original graphDEvery connected graph has at least one spanning tree.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.