Taiwanese Journal of Mathematics

ON CIRCULAR-$L(2,1)$-EDGE-LABELING OF GRAPHS

Abstract

Let $m$, $j$ and $k$ be positive integers with $j \ge k$. An $m$-circular-$L(j,k)$-edge-labeling of a graph $G$ is an assignment $f$ from $\{0,1,\dots,m-1\}$ to the edges of $G$ such that, for any two edges $e_1$ and $e_2$, $|f(e_1)-f(e_2)|_m\geq j$ if $e_1$ and $e_2$ are adjacent, and $|f(e_1)-f(e_2)|_m \geq k$ if $e_1$ and $e_2$ are at distance $2$, where $|a|_m = \min \{a,m-a\}$. The minimum $m$ such that $G$ has an $m$-circular-$L(j,k)$-edge-labeling is defined as the circular-$L(j,k)$-edge-labeling number of $G$, denoted by $\sigma_{j,k}'(G)$. This paper determines the circular-$L(2,1)$-edge-labeling numbers of the infinite $\Delta$-regular tree for $\Delta \ge 2$ and the $n$-dimensional cube for $n \in \{2,3,4,5\}$.

Article information

Source
Taiwanese J. Math., Volume 16, Number 6 (2012), 2063-2075.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406839

Digital Object Identifier
doi:10.11650/twjm/1500406839

Mathematical Reviews number (MathSciNet)
MR3001835

Zentralblatt MATH identifier
1259.05147

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

Citation

Lin, Wensong; Wu, Jianzhuan. ON CIRCULAR-$L(2,1)$-EDGE-LABELING OF GRAPHS. Taiwanese J. Math. 16 (2012), no. 6, 2063--2075. doi:10.11650/twjm/1500406839. https://projecteuclid.org/euclid.twjm/1500406839

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