On self-complementary chordal graphs (Q1383060)

A graph \(G\) is self-complementary (s.c.) if it is isomorphic to its complement. It is known that every such graph has \(p=4n\) or \(p=4n+1\) vertices. At first the authors recall some properties of split graphs and s.c. graphs which are used in this paper. Then they prove, by numerous theorems, structural properties of s.c. graphs which finally yield the following main result (Theorem 19): Let \(G\) be a self-complementary graph. Then \(G\) is a chordal graph iff it has no induced subgraph isomorphic to the cycle \(C_4\) when \(p=4n\); and it has no induced subgraph isomorphic to \(C_4\) or \(C_5\) when \(p=4n+1\).