+4 votes
345 views

Calculate the number of Spanning trees possible for each of these graphs

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I am getting :

1. 81
2. 77
3. 27
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In the 2nd Fig,is O a node or just the pt of intersection of AC and BD?
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Balaji Jegan for 1 i am getting 80.

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@balaji

How bro?
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Getting 64,61,24
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Balaji Jegan in 2nd 5 vertices are there. We need to pick 4 edges from 8. answer will be less than 8c4=70.

How are you getting 77?

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For 1st, 3c2*3c2*3c2*3c2-8 (length 4 cycle) =73
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@balaji

question is not correct

u need to give weight to each edges

Otherwise how do we calculate MST?
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is $(1,2)$ and $(1,3)$ same type of edge ?
+1
@srestha, if we use Kirchoffs algo, why would we require edge weights to determine spanning trees? Qstn didn't ask for min or max spanning tree
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2nd one 69

3rd one 54
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@Sayan

then there will be no cycle

right?

So, 1st one will be $\binom{3}{2}\times \binom{3}{2}\times \binom{3}{2}\times \binom{2}{1}=54$
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2nd one will be

$\binom{4}{3}\times \binom{4}{1}=16$

3rd one will be

$\binom{3}{2}\times \binom{3}{2}\times \binom{2}{1}=18$
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but is spanning tree means , $1$ edge need to be removed from the subgraph?

Spanning tree means , every vertex need to be enclose and also no cycle will be there

right?

So, how can we tell if there is 5 edges, there wouldnot be any cycle?
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srestha mam

if u r referring to link i added then they take care of that case earlier so atlast only 5 edges cases remaining

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I need to draw the graph now

otherwise, I havenot got any error in my answer too.

Is there any answer given @Balaji??

or self doubt?
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self doubt
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then do I give the picture I got?

because it cannot be even checked :(
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@Sayan Bose O is a vertex

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I am getting :

792 - ( 468+32+56+4+4) = 228.

Please help to point out my mistake.

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