PARTITION ENERGY OF SOME TREES AND THEIR GENERALIZED COMPLEMENTS

PARTITION ENERGY OF SOME TREES AND THEIR GENERALIZED COMPLEMENTS

E. Sampathkumar, S. V. Roopa, K. A. Vidya, M. A. Sriraj

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Abstract

Let G = (V;E) be a graph and Pk = fV1; V2; : : : ; Vkg 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 dened 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.

Keywords

Trees, equal degree partition, generalized complements, partition eigenvalues, partition energy.