Seidel energy of iterated line graphs of regular graphs

Abstract

The Seidel matrix S(G) of a graph G is the square matrix whose (i, j)-entry is equal to -1 or 1 if the i-th and j-th vertices of G are adjacent or non-adjacent, respectively, and is zero if i = j. The Seidel energy of G is the sum of the absolute values of the eigenvalues of S(G). We show that if G is regular of order n and of degree r ≥ 3, then for each k ≥ 2, the Seidel energy of the k-th iterated line graph of G depends solely on n and r. This result enables the construction of pairs of non-cospectral, Seidel equienergetic graphs of the same order.