UGC NET CSE | June 2014 | Part 2 | Question: 21

Question

Consider the graph given below as :

Which one of the following graph is isomorphic to the above graph ? 

• A.
• B.
• C.
• D.

Answer 1

From given figure we can say that, every vertex has degree = 3,

in all options but C, graph has at least one vertex with degree = 4

so I think option C would be the correct answer

Comments

C is the ans. Becz it has 12 edges which is equal to above graph edges

---

yes, of course equality of number edges is one of the criterion for showing isomorphish, also we have to take into account degree sequence

Answer 2

The given graph is Bipartite, 3-Regular graph on 8 vertices.

Also the given graph in the question is Hypercube graph on 8 vertices i.e. the given graph is $Q_3.$

Option C is $Q_3$, So option C is correct answer.

We can note that Graph in Option A,B,D have at least one vertex of degree 4, but in the given graph every vertex has degree 3, So, given graph is Not isomorphic to graph in option A,B,D.