SEIDEL ENERGY OF ITERATED LINE GRAPHS OF REGULAR GRAPHS

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.