Seidel Equienergetic Graphs

Abstract

The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are - 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE (G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G1 and G2 are said to be Seidel equienergetic if SE (G1) = SE (G2). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12.