1.

An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if ____________(a) f(u) and f(v) are contained in G but not contained in H(b) f(u) and f(v) are adjacent in H(c) f(u * v) = f(u) + f(v)(d) f(u) = f(u)^2 + f(v)^2This question was addressed to me at a job interview.My enquiry is from Isomorphism in Graphs in section Graphs of Discrete Mathematics

Answer»

The CORRECT choice is (b) f(u) and f(V) are adjacent in H

To elaborate: Two graphs G and H are said to be isomorphic to each other if there exist a one to one CORRESPONDENCE, say f between the vertex sets V(G) and V(H) and aone to one correspondence g between the edge sets E(G) and E(H)with the following conditions:-

(i) for EVERY vertex u in G, there exists a vertex u’ in H such that u’=f(u) and vice versa.

(II) for every edge uv in G, g(uv)=f(u)*f(v)=u’v’ is H.


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