Partition energy of some trees and their generalized complements

Abstract

Let G = (V, E) be a graph and Pk = {V1, V2, . . . , Vk} be a partition of V . The k-partition energy of a graph G with respect to partition Pk is denoted by EPk (G) and is defined as the sum of the absolute values of k-partition eigenvalues of G. In this paper we obtain partition energy of some trees and their generalized complements with respect to equal degree partition. In addition, we develop a matlab program to obtain partition energy of a graph and its generalized complements with respect to a given partition.