Energy of generalized complements of a graph

Sabitha D’souza, H. J. Gowtham, Pradeep G. Bhat

Research output: Contribution to journalArticle

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 ≠ j, remove the edges between Vi and Vj in graph G and add the edges between Vi and Vj which are not in G. The graph GPk thus obtained is called the 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 (formula presented) 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.

Original languageEnglish
Pages (from-to)131-136
Number of pages6
JournalEngineering Letters
Volume28
Issue number1
Publication statusPublished - 01-01-2020

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Fingerprint Dive into the research topics of 'Energy of generalized complements of a graph'. Together they form a unique fingerprint.

  • Cite this

    D’souza, S., Gowtham, H. J., & Bhat, P. G. (2020). Energy of generalized complements of a graph. Engineering Letters, 28(1), 131-136.