A defective vertex coloring of a graph is a coloring in which some adjacent vertices may have the same color. An edge whose adjacent vertices have the same color is called a bad edge. A defective coloring of a graph $G$ with minimum possible number of bad edges in $G$ is known as a near proper coloring of $G$. In this paper, we introduce the notion of equitable near proper coloring of graphs and determine the minimum number of bad edges obtained from an equitable near proper coloring of some graph classes.
[1] F. Harary, Graph Theory, Narosa Publ. House, New Delhi, 1996.
[2] J. Kok and N.K. Sudev, δ(k)- colouring of cycle related graphs, Adv. Stud. Contemp. Math. 32 (2022), no. 1, 113–120.
[3] S. Naduvath and M. Ellumkalayil, A note on δ(k)-colouring of the cartesian product of some graphs, Commun. Comb. Optim. 7 (2022), no. 1, 113–120. https://doi.org/10.22049/cco.2021.27114.1211
[4] D.B. West, Introduction to graph theory, Prentice Hall of India, New Delhi, 2001.
Jose, S., Samuel, L., & Naduvath, S. (2024). On Equitable Near Proper Coloring of Graphs. Communications in Combinatorics and Optimization, 9(1), 131-143. doi: 10.22049/cco.2022.27240.1218
MLA
Sabitha Jose; Libin Chacko Samuel; Sudev Naduvath. "On Equitable Near Proper Coloring of Graphs". Communications in Combinatorics and Optimization, 9, 1, 2024, 131-143. doi: 10.22049/cco.2022.27240.1218
HARVARD
Jose, S., Samuel, L., Naduvath, S. (2024). 'On Equitable Near Proper Coloring of Graphs', Communications in Combinatorics and Optimization, 9(1), pp. 131-143. doi: 10.22049/cco.2022.27240.1218
VANCOUVER
Jose, S., Samuel, L., Naduvath, S. On Equitable Near Proper Coloring of Graphs. Communications in Combinatorics and Optimization, 2024; 9(1): 131-143. doi: 10.22049/cco.2022.27240.1218
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