L(3,2,1)-labelings of three classes of 4-valent circulants
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916005161205760 |
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| author | Holub, Přemysl Kopřiva, Martin |
| author_facet | Holub, Přemysl Kopřiva, Martin |
| contents | An $L(3,2,1)$-labeling of a graph $G$ is an assignment $f$ of nonnegative integers to vertices such that $\vert f(x)-f(y)\vert > 3-\mbox{dist}_G(x,y)$ for every pair $x,y$ of vertices of $G$, where $\mbox{dist}_G(x,y)$ denotes the distance between $x$ and $y$ in $G$. The minimum span (i.e., the difference between the largest and the smallest value) among all $L(3,2,1)$-labelings of $G$ is denoted by $λ_{(3,2,1)}(G)$. In this paper, we study $L(3,2,1)$-labelings of three classes of circulant graphs. Namely, we investigate $λ_{(3,2,1)}$ of circulant graphs $C_n(1,t)$, where $t\in\{3,4,5\}$ and $n$ is the order of the graph. This paper is a continuation of a recent publications of V. Bianco and T. Calamoneri who studied the square of cycles, i.e., circulant graphs $C_n(1,2)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_12574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | L(3,2,1)-labelings of three classes of 4-valent circulants Holub, Přemysl Kopřiva, Martin Combinatorics 05C12, 05C15, 05C78 An $L(3,2,1)$-labeling of a graph $G$ is an assignment $f$ of nonnegative integers to vertices such that $\vert f(x)-f(y)\vert > 3-\mbox{dist}_G(x,y)$ for every pair $x,y$ of vertices of $G$, where $\mbox{dist}_G(x,y)$ denotes the distance between $x$ and $y$ in $G$. The minimum span (i.e., the difference between the largest and the smallest value) among all $L(3,2,1)$-labelings of $G$ is denoted by $λ_{(3,2,1)}(G)$. In this paper, we study $L(3,2,1)$-labelings of three classes of circulant graphs. Namely, we investigate $λ_{(3,2,1)}$ of circulant graphs $C_n(1,t)$, where $t\in\{3,4,5\}$ and $n$ is the order of the graph. This paper is a continuation of a recent publications of V. Bianco and T. Calamoneri who studied the square of cycles, i.e., circulant graphs $C_n(1,2)$. |
| title | L(3,2,1)-labelings of three classes of 4-valent circulants |
| topic | Combinatorics 05C12, 05C15, 05C78 |
| url | https://arxiv.org/abs/2601.12574 |