DM-Graphs-Q5

Question

Which of the following graphs are isomorphic?

(A). Graph 1 and Graph 4

(B). Graph 2 and Graph 3

(C). Graph 1 and Graph 3

(D). Graph 2 and Graph 4

Answer 1

(B). Graph 2 and Graph 3

(C). Graph 1 and Graph 3

I think both are right.

@Kiran sir, please verify

Reference: http://mathworld.wolfram.com/WagnerGraph.html

Comments

but same degree sequence does not imply that they are isomorphic.
Not having same degree implies that they are not isomorphic

p --> q   is not eq. to its inverse   ~p --> ~q

therefore graph 4 is out of question, but how to differentiate between the graphs 1,2,3

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Yes, you are right, I'm trying to find a number of cycles.

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I also agree

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@Kiran sir please correct it where I'm wrong?

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bro in graph 4 f and h both have degree 4

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if anyone wants to join our discussion group
https://chat.whatsapp.com/KioGCcB8oSIHF17pElhyYZ

Answer 2

heres an easy solution

A) 1 and 4 are not isomorphic (iv has 3-length cycle but i does not)

D) similarly 2 and 4 are not isomorhic(ii does not have 3-length cycle)

C) also 1and 3 are not isomorphic( iii has 5-length cycle which is absent in i)

so A,C,D are are wrong, remaining is B which must be the answer. comment if you find any thing wrong

Comments

@tsabhineetsingh192 i think (i) has cycle of length 5 h-a-b-c-d-h

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I think (i) and (iii) are not isomorphic bcoz in (iii) there can be maximum 3 cycles of length 4 and in (i) there can be more than 3 cycles of length 4,correct me if am wrong

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Yes, 1 has five length cycle. I didn't see it. Thx for pointing out

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How only 3 in i) ( bcgfb ,cdhgc, deahd, efbae)

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@tsabhineetsingh192 bro read my comment once again ,
"I think (i) and (iii) are not isomorphic bcoz in (iii) there can be maximum 3 cycles of length 4 and in (i) there can be more than 3 cycles of length 4"