Type: Article

Graphs whose complement and square are isomorphic

Milanic, Martin; Pedersen, Anders Sune; Pellicer, Daniel; et al.;

Abstract:

We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-complementary graphs, and characterize square-complementary graphs within various graph classes. The bipartite case turns out to be of particular interest. We also exhibit a square-complementary graph with a triangle, thus answering in the affirmative a question asked independently by Baltic et al. and by Capobianco and Kim. (C) 2014 Elsevier B.V. All rights reserved.