How many spanning trees of the graph contain the edges QS and RS?
I am not so sure on how to solve this question because there are some many different spanning tree I suppose. Precisely how do I solve questions like this? Thank you.
2026-04-01 19:43:38.1775072618
Graph Theory(Spanning Tree)
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A spanning tree is a set of edges that connect all the vertices but don't create any cycles. Equivalently, you need exactly $n-1$ edges (where $n$ is the number of vertices) and a route from any vertex to any other.
Once you have QS and RS, you need two more edges. Also, Q, R and S are already connected to each other. So you need to connect P and T. Since there is no edge PT, the only way to do this is to use one edge to connect P to Q/R/S, and another to connect T to Q/R/S. There are $3$ choices for the first edge, but only $2$ for the second (since TR doesn't exist), so there are $6$ ways to make both choices.