Range of Diameters of a Bipartite Graph and its Generalized 2-Partite Internal Complement

Abstract

Complements of graphs, more particularly self-complementary graphs, have been extensively studied by many mathematicians, H. Sachs ([9], G. Ringel ([8]), C.R.J. Clapham ([1]), Gibs ([4]), S.B. Rao ([7]), T. Gangopadhyay ([2, 3]) etc. being the more prominent ones. Many problems such as the Hamiltonian problem, the characterization of potentially and forcibly self-complementary degree sequences have been solved for this class of graphs (see references given in [7]). Similar problems have been studied for the class of bipartite/multipartite graphs.