Seidel polynomial and energy of join of two graphs

Abstract

For a graph G, Seidel matrix is defined as S(G)=[s_ij] in which s_ij=-1 if the vertices v_i and v_j are adjacent, [s_ij]=1 if the vertices v_i and v_j are not adjacent and [s_ij]=0 for i=j. Seidel polynomial is the polynomial associated to the Seidel matrix. In the present work, we study Seidel polynomial for join of any two graphs by using the concept of coronal of a matrix and hence construct a pair of Seidel equienergetic graphs by joining a regular graph (which is among a pair of Seidel equienergetic graphs of same order and degree) with a non-regular graph.