The conjugate characteristic polynomial of some compound graphs

Abstract

Let G be a simple graph of order n and let S be any subset of the vertex set V(G). We denote by G S, T the graph obtained from G by adding two new non-adjacent vertices x, y, so that x is adjacent exactly to the vertices from S, and y is adjacent exactly to the vertices from T, where T=V(G)∖S. We here determine the conjugate characteristic polynomial of the graph G S, T . We also consider some other compound graphs obtained from G and determine their conjugate characteristic polynomials.