HARARY ENERGY OF COMPLEMENT OF LINE GRAPHS OF REGULAR GRAPHS

Abstract

The Harary matrix of a graph G is deÖned as H(G) = [hij ], wherehij = 1d(vi;vj ), if i 6= j and hij = 0, otherwise, where d(vi; vj ) is the distancebetween the vertices vi and vj in G. The H-energy of G is deÖned as thesum of the absolute values of the eigenvalues of Harary matrix. Two graphsare said to be H-equienergetic if they have same H-energy. In this paper weobtain the H-energy of the complement of line graphs of certain regular graphsin terms of the order and regularity of a graph and thus constructs pairs ofH-equienergetic graphs of same order and having di§erent H-eigenvalues.