A Characterization of Forcibly Tripartite Self-Complementary class of Partitioned Sequences

Degree Sequences of self-complementary(sc) graphs have been studied by many, to mention a few : C. R. J. Clapham and D. J. Kleitman [2], S. B. Rao [12] and A. Farrugia [3]. Frank Harary [6, 7] gives a generating function for counting non-isomorphic graphs and chromatically non-isomorphic bigraphs with given number of edges. It is mentioned in [7] that the problem remains open for r-partite graphs with r > 2. But he gives a generating function for chromatically non-isomorphic tri-partite graphs with unequal sizes of three parts. K. R. Parthasarathy [10] gives a generating function for counting non-isomorphic graphs and chromatically non-isomorphic bipartite graphs with a given partition. He [11] also gives a generating function for counting non-isomorphic self-complementary graphs. N. S. Bhave and T. T. Raghunathan [1] extended the results of this paper and gave a generating function for counting chromatically non-isomorphic bipartite self-complementary(bsc) graphs with a given bipartition.