  Graph isomorphism is an important computer science problem. The problem for
the general case is unknown to be in polynomial time. The base algorithm for
the general case works in quasi-polynomial time. The solutions in polynomial
time for some special type of classes are known. In this work, we have worked
with a special type of graphs. We have proposed a method to represent these
graphs and finding isomorphism between these graphs. The method uses a modified
version of the degree list of a graph and neighbourhood degree list. These
special type of graphs have a property that neighbourhood degree list of any
two immediate neighbours is different for every vertex.The representation
becomes invariant to the order in which the node was selected for giving the
representation making the isomorphism problem trivial for this case. The
algorithm works in $O(n^4)$ time, where n is the number of vertices present in
the graph. The proposed algorithm runs faster than quasi-polynomial time for
the graphs used in the study.
