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Cospectral and hyper-energetic self complementary comparability graphs
Merajuddin,S. A. K. Kirmani,Parvez Ali,S. Pirzada 한국산업응용수학회 2007 Journal of the Korean Society for Industrial and A Vol.11 No.3
A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted X(H)) equals the number of vertices in the largest clique in H (denoted w(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (sec) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic sec graphs with n vertices each, (n < 13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic sec graph is 13.
Cospectral and hyper-energetic self complementary comparability graphs
( Merajuddin ),( S. A. K. Kirmani ),( Parvez Ali ),( S. Pirzada ) 한국산업응용수학회(구 한국산업정보응용수학회) 2007 한국산업정보응용수학회 Vol.11 No.3
A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted X(H)) equals the number of vertices in the largest clique in H (denoted w(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n < 13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.