Korean J. Math.  Vol 23, No 4 (2015)  pp.607-618
DOI: https://doi.org/10.11568/kjm.2015.23.4.607

Distance two labeling on the square of a cycle

Xiaoling Zhang

Abstract


An $L(2,1)$-labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all non-negative integers such that $|f(u)-f(v)|\geq 2$ if $d(u,v)=1$  and $|f(u)-f(v)|\geq 1$ if $d(u,v)=2$. The $\lambda$-number  of $G$, denoted $\lambda(G)$, is the smallest number $k$ such that $G$ admits an $L(2, 1)$-labeling with $k=\max\{f(u)|u\in V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its $\lambda$-number. In addition, we also completely determine its edge span.

Keywords


Channel assignment; $L(2,1)$-labeling; square of a cycle; $\lambda$-number; edge span.

Subject classification

05C15

Sponsor(s)

Research supported by Science Foundation of the Fujian Province, China (No. 2015J05013).

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