Color Energy of Generalised Complements of a Graph

Swati Nayak, Sabitha D’Souza, H. J. Gowtham, Pradeep G. Bhat

Research output: Contribution to journalArticlepeer-review

Abstract

The color energy of a graph is defined as sum of absolute color eigenvalues of graph, denoted by EC(G). Let Gc = (V, E) be a color graph and P = {V1, V2,…,Vk} be a partition of V of order k≥1. The k-color complement {Gc}k p of Gc is defined as follows: For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj and add the edges which are not in Gc such that end vertices have different colors. For each set Vr in the partition P, remove the edges of Gc inside Vr, and add the edges of Gc (the complement of Gc) joining the vertices of Vr. The graph {Gc}P k(i) thus obtained is called the k(i)— color complement of Gc with respect to the partition P of V. In this paper we characterize generalized color complements of some graphs. We also compute color energy of generalised complements of star, complete, complete bipartite, crown, cocktail party, double star and friendship graphs.

Original languageEnglish
JournalIAENG International Journal of Applied Mathematics
Volume50
Issue number4
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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