Spanning Trees

Question

Consider the following adjacency matrix representation of connected graph then find the number of spanning trees are possible for the given graph
$\begin{bmatrix} 0&1&1&1&0 \\  1&0&1&1&0 \\1&1&0&0&1 \\ 1&1&0&0&1 \\0&0&1&1&0 \end{bmatrix}$

Comments

24 ?

Answer 1

Here one more loop containing number of edges = 4 which is 1 - 3 - 2 - 4 - 1 ..So this has to be subtracted as well

Hence number of spanning trees should be equal to 24

Comments

Ya I agree that depends on perspective as well..As Kirchoff's method also involves matrix operations so it will also take time possibly for larger graphs..:)

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Yes, but always give preference to a method which is less error prone even if a bit more time consuming.

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Ok sir..Agreed..:)