Question

Count the total number of spanning trees of the following graphs, with justification. (a) The n-cycle, for any n≥3.

Answer 1

The number of spanning trees of an n-cycle graph for any n≥3 is n, as each edge removal creates a unique spanning tree.

Step-by-step explanation:

To count the total number of spanning trees of an n-cycle graph for any n≥3, you can use the formula derived from the matrix-tree theorem. For an n-cycle graph, which is a graph that forms a single loop of n nodes, there are n spanning trees. This is because you can remove any one edge to create a spanning tree, and since there are n edges, there are n different ways to do this, resulting in n different spanning trees.