Certain chromatic sums of some cycle-related graph classes
Abstract
Let 𝒞={c1,c2,c3,…,ck} be a certain type of proper k-coloring of a given graph G and θ(ci) denote the number of times a particular color ci is assigned to the vertices of G. Then, the coloring sum of a given graph G with respect to the coloring 𝒞, denoted by ω𝒞(G), is defined to be ω(𝒞)=∑ki=1iθ(ci). The coloring sums such as χ-chromatic sum, χ+-chromatic sum, b-chromatic sum, b+-chromatic sum, etc. are some of these types of coloring sums that have been studied recently. Motivated by these studies on certain chromatic sums of graphs, in this paper, we study certain chromatic sums for some standard cycle-related graphs.
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