PARTITION ENERGY OF SOME TREES AND THEIR GENERALIZED COMPLEMENTS

Let G = (V, E) be a graph and [P.sub.k] = {[V.sub.1],[V.sub.2],...,[V.sub.k]} be a partition of V. The k-partition energy of a graph G with respect to partition [P.sub.k] is denoted by [mathematical expression not reproducible] (G) and is defined as the sum of the absolute values of k-partition eige...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2020-04, Vol.10 (2), p.521
Main Authors: Sampathkumar, E, Roopa, S.V, Vidya, K.A, Sriraj, M.A
Format: Article
Language:English
Subjects:
Eigenvalues
Graph theory
Mathematical research
Online Access:Get full text
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Summary:Let G = (V, E) be a graph and [P.sub.k] = {[V.sub.1],[V.sub.2],...,[V.sub.k]} be a partition of V. The k-partition energy of a graph G with respect to partition [P.sub.k] is denoted by [mathematical expression not reproducible] (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. Keywords: Trees, equal degree partition, generalized complements, partition eigenvalues, partition energy. AMS Subject Classification: 05C70,05C05,05C50
ISSN:2146-1147