2026· International Journal of Mathematical and Computer Sciences· 0 citations· 10 references
Abstract
An equitable k-coloring is a proper coloring with color classes V_1,V_2,\ldots,V_{k} for which the numbers of vertices in any two color classes differ by at most one. A graph G is equitably k-colorable if there is an equitable k-coloring. The smallest positive integer k such that G is equitably k-colorable is the equitable chromatic number of G, denoted by \chi_{=}(G). The derived graph of a simple graph, denoted by G^+, is the graph having the same vertex set as G, in which two vertices are adjacent if and only if their distance in G is two. In this paper, we determine the exact values of the equitable chromatic number of the derived graph of paths, cycles, wheel graphs, helm graphs, sunlet graphs, and tadpole graphs.
This paper introduces the concept of the power dominator equitable coloring, which combines the monitoring capability of power dominator coloring with the balanced partition requirement of equitable coloring. A proper coloring is called a power dominator equitable coloring if every vertex power dominates at least one c...
G. Navamani, L. Jacquline, N. Revathi et al.· International Journal of Ana...· 0 citations
An acyclic edge coloring of a graph G is a proper edge coloring such that G contains no bichromatic cycles. The acyclic chromatic index χa′(G) is the minimum number of colors required for an acyclic edge coloring. Fiamčik and Alon et al. independently conjectured that χa′(G)≤Δ+2 for every simple graph G with maximum de...
Given a graph G , an r -hued coloring of G is a proper vertex coloring such that for every vertex v , the number of colors appearing in its neighborhood is at least min { d G ( v ) , r } , where d G ( v ) denotes the degree of v in G . The r -hued chromatic number χ r ( G ) is the smallest number of colors needed for a...
The dominated coloring of a graph $G$ is a proper vertex coloring such that each color class is dominated by a vertex. The minimum number of colors required for a dominated coloring of a graph $G$ is called the dominated chromatic number of the graph $G$ and is denoted by $\chi_{dom}(G)$. A graph $G$ is said to be chro...
We introduce and begin the study of sequence b-colorings, a natural generalization of the classical notion of b-colorings introduced by Irving and Manlove in 1999. In a sequence b-coloring, each color class is required to contain a prescribed minimum number of color-dominating vertices (CDVs). We establish several fund...
An interval edge coloring of a graph is a proper edge coloring by integers such that the colors on the edges incident with any vertex form an interval of integers. Not all graphs are interval colorable; a simple counterexample is $K_3$. The (interval coloring) deficiency of a graph $G$ is the minimum number of pendant...
C. J. Casselgren, P. Petrosyan· 0 citations
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