  In this paper we develop three characterizations for isomorphism of graphs.
The first characterization is obtained by associating certain bitableaux with
the graphs. We order these bitableaux by suitably defined lexicographic order
and denote the bitableau that is least in this order as the standard
representation for the associated graph. The standard representation
characterizes graphs uniquely. The second characterization is obtained in terms
of associated rooted, unordered, pseudo trees. We show that the isomorphism of
two given graphs is implied by the isomorphism of their associated pseudo
trees. The third characterization is obtained in terms of ordered adjacency
lists to be associated with two given labeled graphs. We show the two given
labeled graphs are isomorphic if and only if their associated ordered adjacency
lists can be made identical by the action of suitable transpositions on any one
of these lists. We discuss in brief the complexity of these characterizations
described in this paper for deciding isomorphism of graphs. Finally, we discuss
the k-clique problem in the light of these characterizations towards the end of
the paper.
