Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.
Question
Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.
Solution
A complete graph with 4 vertices is also known as K4. The number of spanning trees for a complete graph with n vertices is given by the formula n^(n-2).
So, for a complete graph with 4 vertices, the number of spanning trees is 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
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.
Every graph has only one minimum spanning tree. State true or false.a)Trueb)False
Define spanning tree
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 __.
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