Affiliation:
1. Mathematics Department, SUNY Buffalo State, Buffalo, NY 14222, USA
2. School of Business, State University of New York at Fredonia, Fredonia, NY 14063, USA
Abstract
In this paper, we study the class of graphs Gm,n that have the same degree sequence as two disjoint cliques Km and Kn, as well as the class G¯m,n of the complements of such graphs. The problems of finding a maximum clique and a maximum independent set are NP-hard on Gm,n. Therefore, looking for upper and lower bounds for the clique and independence numbers of such graphs is a challenging task. In this article, we obtain such bounds, as well as other related results. In particular, we consider the class of regular graphs, which are degree-equivalent to arbitrarily many identical cliques, as well as such graphs of bounded degree.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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