On $L(1,2)$-Edge-Labelings of Some Special Classes of Graphs
Received:July 06, 2013  Revised:March 19, 2014
Key Words: $L(j,k)$-edge-labeling   line graph   path   cycle   complete graph   complete multipartite graph   infinite $\Delta$-regular tree   wheel.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10971025; 10901035).
Author NameAffiliation
De HE Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China 
Wensong LIN Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China 
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Abstract:
      For a graph $G$ and two positive integers $j$ and $k$, an $m$-$L(j,k)$-edge-labeling of $G$ is an assignment on the edges to the set $\{0,\ldots,m\}$, such that adjacent edges receive labels differing by at least $j$, and edges which are distance two apart receive labels differing by at least $k$. The $\lambda^{\prime}_{j,k}$-number of $G$ is the minimum $m$ of an $m$-$L(j,k)$-edge-labeling admitted by $G$. In this article, we study the $L(1,2)$-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite $\Delta$-regular trees and wheels.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.04.003
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