Packing chromatic number of unitary Cayley graphs of $\Bbb Z_n$ and algorithmic approaches to it
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913828666605568 |
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| author | Hamed-Labbafian, Zahra Tavakoli, Mostafa Afkhami, Mojgan Klavžar, Sandi |
| author_facet | Hamed-Labbafian, Zahra Tavakoli, Mostafa Afkhami, Mojgan Klavžar, Sandi |
| contents | A packing $k$-coloring of a graph $G$ is a partition of $V(G)$ into $k$ disjoint non-empty classes $V_1, \dots, V_k$, such that if $u,v \in V_i$, $i\in [k]$, $u\ne v$, 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 $\mathbb{Z}_n$ is computed. Two metaheuristic algorithms for calculating the packing chromatic number are also proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Packing chromatic number of unitary Cayley graphs of $\Bbb Z_n$ and algorithmic approaches to it Hamed-Labbafian, Zahra Tavakoli, Mostafa Afkhami, Mojgan Klavžar, Sandi Combinatorics A packing $k$-coloring of a graph $G$ is a partition of $V(G)$ into $k$ disjoint non-empty classes $V_1, \dots, V_k$, such that if $u,v \in V_i$, $i\in [k]$, $u\ne v$, 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 $\mathbb{Z}_n$ is computed. Two metaheuristic algorithms for calculating the packing chromatic number are also proposed. |
| title | Packing chromatic number of unitary Cayley graphs of $\Bbb Z_n$ and algorithmic approaches to it |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.06099 |