On extension of regular graphs

Abstract

In this article, we discuss when one can extend an r-regular graph to an r + 1 regular by adding edges. Different conditions on the number of vertices n and regularity r are developed. We derive an upper bound of r, depending on n, for which, every regular graph G(n, r) can be extended to an r + 1-regular graph with n vertices. Presence of induced complete bipartite subgraph and complete subgraph is discussed, separately, for the extension of regularity.