On Color Energy of Few Classes of Bipartite Graphs and Corresponding Color Complements

Prajakta Bharat Joshi; Mayamma Joseph

doi:10.15415/mjis.2019.81002

Authors

Prajakta Bharat Joshi Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India
Mayamma Joseph Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India

DOI:

https://doi.org/10.15415/mjis.2019.81002

Keywords:

Color eigenvalues, color energy, color complement

Abstract

For a given colored graph G, the color energy is defined as Ec(G) = Σλ_i, for i = 1, 2,…., n; where λ_i is a color eigenvalue of the color matrix of G, A_c (G) with entries as 1, if both the corresponding vertices are neighbors and have different colors; -1, if both the corresponding vertices are not neighbors and have same colors and 0, otherwise. In this article, we study color energy of graphs with proper coloring and L (h, k)-coloring. Further, we examine the relation between E_c(G) with the corresponding color complement of a given graph G and other graph parameters such as chromatic number and domination number.

AMS Subject Classification: 05C15, 05C50

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