Research Article

Packing chromatic number of unitary cayley graphs of ℤ _n and algorithmic approaches to it

Published in: Quaestiones Mathematicae
Volume 49 , issue 7 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 987–999

DOI: 10.2989/16073606.2026.2630104

Author(s): Mojgan AfkhamiDepartment of Mathematics, University of Neyshabur, Iran, Zahra Hamed-LabbafianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran, Sandi KlavžarFaculty of Mathematics and Physics, University of Ljubljana, Slovenia, and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia, and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia, Mostafa TavakoliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran,

Keywords: 05C15, 05C85,

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Abstract

A packing k-coloring of a graph G is a partition of V (G) into k disjoint non-empty classes V ₁, … , V_k , such that if u, v ∈ V_i , i ∈ [k], u ≠ v then the distance between u and v is greater than i. The packing chromatic number of G is the smallest integer k which admits a packing k-coloring of G. In this paper, the packing chromatic number of the unitary Cayley graph of ℤ _n is computed. Two metaheuristic algorithms for calculating the packing chromatic number are also proposed.

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