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29 votes

Which of the following graphs is isomorphic to 

 





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4 Answers

Best answer
44 votes
44 votes

For these type of questions find which are not isomorphic.

The graph in option (A) has a $3$ length cycle whereas the original graph does not have a $3$ length cycle
The graph in option (C) has vertex with degree $3$ whereas the original graph does not have a vertex with degree $3$
The graph in option (D) has a $4$ length cycle whereas the original graph does not have a $4$ length cycle

so option B must be correct.

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7 votes
7 votes

Ans: (B)

Explanation: Degree sequence of the given graph 4-2-2-2-2-2-1-1.

Degree sequene for other options: 

     A) 4-3 failed

    C)  3- failed

    For B) and D) degree sequence matches with given 4-2-2-2-2-2-1-1. Comparing B) , D) and original graph: original graph has 5-cycle. But D) have only 4-cycle. 

    B) matches all the criterias for isomorphic graph.

5 votes
5 votes
if graphs have to be isomorphic then they must follow the three condition

(1) no of points must be same

(2) no of edges also must be same

(3) degree sequence must be same

if these three conditon is following simultaneously then graph will be isomorpphic

option b is correct
2 votes
2 votes
For Isomorphic :i)No of edges must be same ii)No of vertices must be same  iii)And Pendant vertex same too

all options have equal number of edges and vertices but the thing which differ it from right one is pendant vertex

In given graph a node which have pendant vertex is 4 and 1 vertex has 2 nodes and another is one so option B contains same so option B is right one
Answer:

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