Abstract. Given a colored graph G, its color energy E c (G) is defined as the sum of the absolute values of the eigenvalues of the color matrix of G. The concept of color energy was introduced by Adiga et al. [1]. In this article, we obtain some new bounds for the color energy of graphs and establish relationship between color energy E c (G) and energy E(G) of a graph G. Further, we construct some new families of graphs in which one is non-co-spectral color-equienergetic with some families of graphs and another is color-hyperenergetic. Also we derive explicit formulas for their color energies.
Given a graph G = (V, E), with respect to a vertex partition π« we associate a matrix called π«-matrix and define the π«-energy, Eπ« (G) as the sum of π«-eigenvalues of π«-matrix of G. Apart from studying some properties of π«-matrix, its eigenvalues and obtaining bounds of π«-energy, we explore the robust(shear) π«-energy which is the maximum(minimum) value of π«-energy for some families of graphs. Further, we derive explicit formulas for Eπ« (G) of few classes of graphs with different vertex partitions.
Ξ» where Ξ» 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 color energy of the color complement of a given graph G and other graph parameters such as chromatic number and domination number.
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