Abstract
For a given colored graph G, the color energy is defined as Ec(G) = Σλi, for i = 1, 2,…., n; where λi is a color eigenvalue of the color matrix of G, Ac (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 Ec(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
Highlights
We consider throughout this paper only undirected graphs with order n and size m, which are simple and finite
We study color energy of graphs with proper coloring and L (h, k)-coloring
We examine the relation between Ec(G) with the color energy of the color complement of a given graph G and other graph parameters such as chromatic number and domination number
Summary
We consider throughout this paper only undirected graphs with order n and size m, which are simple and finite. For related concepts and definitions, we refer to In 2013, Adiga et al (Adiga, Sampathkumar, Sriraj and Shrikanth 2013) initiated the study of color matrix. Adiga et al (Adiga, Sampathkumar, Sriraj and Shrikanth 2013) defined color energy Ec(G) for a colored graph G as the sum of the absolute values of color eigenvalues of the color matrix of G. For the last few years the concept of color energy has been considerably studied and new variations of the same have been introduced The study includes determination of color energy of a bistar Bq,q of order n = 2q and some other families of graphs as well as their color complements.
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