On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc - I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Sajna in 2004. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost selfcomplementary vertex-transitive graphs, and non-cyclically almost self-complementary circulant graphs.

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Primoz Potocnik, Mateja Sajna
• Keywords: Circulant Graphs, DM 2006, Self-complementary Circulant Graphs, Self-complementary Regular Graphs