Last Updated : 19 Nov, 2018
Find the total number of possible spanning trees in given graph:
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(A) 10 (B) 11 (C) 12 (D) 13

Answer: (B)

Explanation: Possible number of spanning trees for given graph are as following below:
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Therefore, option (B) 11 is the correct answer. Alternative method: Using matrix as given method: \\begin{bmatrix} 2 & -1 & -1 & 0 & 0\\\\ -1 & 2 & 0 & -1 & 0\\\\ -1 & 0 & 3 & -1 & -1\\\\ 0 & -1 & -1 & 3 & -1\\\\ 0 & 0 & -1 & -1 & 2 \\end{bmatrix} So, co-fatcor of 1×1 in above matrix is: \\begin{bmatrix} 2 & 0 & -1 & 0\\\\ 0 & 3 & -1 & -1\\\\ -1 & -1 & 3 & -1\\\\ 0 & -1 & -1 & 2 \\end{bmatrix} So, determinant of above 4×4 matrix is 11, which is answer.

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