Energy of Generalized Complements of a Graph

Dsouza, Sabitha and Gowtham, H J and Bhat, Pradeep G (2020) Energy of Generalized Complements of a Graph. Engineering Letters, 28 (1). ISSN 1816-093X

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Abstract

Let G be a finite simple graph on n vertices. Let P = {V1,V2,V3,...,Vk} be a partition of vertex set V (G) of order k ≥ 2. For all Vi and Vj in P, i 6= j, remove the edges between Vi and Vj ingraph G andaddtheedgesbetween Vi and Vj whicharenotin G.Thegraph GP k thusobtainediscalledthe k−complement of graph G with respect to the partition P. Let P = {V1,V2,V3,...,Vk} be a partition of vertex set V (G) of order k ≥ 1. For each set Vr in P, remove the edges of graph G inside Vr and add the edges of G (the complement of G) joining the vertices of Vr. The graph GP k(i) thus obtained is called the k(i)−complement of graph G with respect to the partition P. Energy of a graph G is the sum of absolute eigenvalues of G. In this paper, we study energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in energy due to changes in the partition of the graph

Item Type: Article
Uncontrolled Keywords: generalized complements, spectrum, energy
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 17 Mar 2020 08:41
Last Modified: 17 Mar 2020 08:41
URI: http://eprints.manipal.edu/id/eprint/155005

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