| Issue |
RAIRO-Oper. Res.
Volume 56, Number 6, November-December 2022
|
|
|---|---|---|
| Page(s) | 3845 - 3852 | |
| DOI | https://doi.org/10.1051/ro/2022186 | |
| Published online | 11 November 2022 | |
On r-hued coloring of product graphs
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P.R. China
* Corresponding author: xjulfx@163.com
Received:
25
December
2021
Accepted:
22
October
2022
A (k,r)-coloring of a graph G is a proper coloring with k colors such that for every vertex v with degree d(v) in G, the color number of the neighbors of v is at least min{d(v),r}. The smallest integer k such that G has a (k,r)-coloring is called the r-hued chromatic number and denoted by χr(G). In Kaliraj et al. [Taibah Univ. Sci. 14 (2020) 168–171], it is determined the 2-hued chromatic numbers of Cartesian product of complete graph and star graph. In this paper, we extend its result and determine the r-hued chromatic number of Cartesian product of complete graph and star graph.
Mathematics Subject Classification: 05C15 / 05C76
Key words: (k,r)-coloring / r-hued chromatic number / Cartesian product
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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