The complete graph $K_{n}$ has ________ different spanning trees.

n^{n - 2}

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n x n

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n_{n}

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n_{2}

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Solution

The correct option is A $n^{n - 2}$

The complete graph Kn has n^n-2 different spanning trees.

If a graph is a complete graph with n vertices, then total number of spanning trees is n^^(n-2) where n is the number of nodes in the graph.

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with graph vertices is denoted and has undirected edges, where is a binomial coefficient.

A spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges.

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