please explain

Question

Number of spanning trees for the following graph is

(a) 5                                                                             (b) 6

(c) 8                                                                             (d) 9

solution: using kirchoff theorem 

i have got this matrix 

please explain how to solve this matrix to find co factor ans solve it

Comments

8 answer)

brother there was no nee to use kirchoff,s here...

you can just simplify it...

step 1) forget about the edge de as it will be included in every MST.

step 2) now from the polygon abcd having 5 edges try to find the MST.

     ( you will observe that u will get 3 different  MST each having two having pair and one having quad)

...................................................................................................................

or ......

now you can apply kirchoff's with four vertices abcd and find the determinant of any 3*3 matrix of 4*4 it will be easier.(though i don't prefer this method)

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@arvin  I think answer is 8. Please verify

@Mak Indus Avoid using Kirchoff theorem, it takes plenty of time. Still, if you want to know how it works:

Co-factor of $M_{00}$ = 1* Det(A) + (-1)Det(B) = 8

Determinant of A = 13

3	-1	-1
-1	2	-1
-1	-1	4

Determinant of B = 5

3	-1	1
-1	2	-1
0	0	-1

 

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@shreyansh jain thanku brother for correcting. yes i missed that there.