Color Energy of Generalised Complements of a Graph

The color energy of a graph is defined as sum of absolute color eigenvalues of graph, denoted by E_C(G). Let G_c = (V, E) be a color graph and P = {V₁, V₂,…,V_k} be a partition of V of order k≥1. The k-color complement {G_c}k ^p of G_c is defined as follows: For all V_i and V_j in P, i ≠ j, remove the edges between V_i and V_j and add the edges which are not in Gc such that end vertices have different colors. For each set V_r in the partition P, remove the edges of Gc inside V_r, and add the edges of Gc (the complement of G_c) joining the vertices of V_r. The graph {G_c}^P _k(i) thus obtained is called the k(i)— color complement of G_c with respect to the partition P of V. In this paper we characterize generalized color complements of some graphs. We also compute color energy of generalised complements of star, complete, complete bipartite, crown, cocktail party, double star and friendship graphs.