New upper bounds on the L(2, 1)-labeling of the skew and converse skew product graphs
New upper bounds on the L(2, 1)-labeling of the skew and converse skew product graphs
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偏斜和逆偏斜积图的 L(2, 1) 标记的新上限
DOI：
10.1016/j.tcs.2011.01.031
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发表时间：
2011
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影响因子：
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通讯作者：
Cuiqi Wang
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作者：
Ziming Duan;Pingli Lv;L. Miao;Z. Miao;Cuiqi Wang
图G的L（2,1）标记被定义为从顶点集V(G)到非负整数的函数f，使得对于任意两个顶点x，y, |f(x)−f(y)|≥2，如果d(x,y)=2, |f(x)−f(y)|≥1，如果d(x,y)=2，其中d（x,y）是G中x和y之间的距离，G的L（2,1）标记数λ2,1(G)是最小的数k，使得G具有L（2,1）标记，k=max{f(x)|x∈V(G)}。本文考虑由两个图的斜积和逆斜积构成的图，给出了L（2,1）标记数的上界，改进了Shao和Zhang [z.d]所得到的上界邵，张德华，斜与逆斜积图的L（2,1）标记的改进上界，定理。第一版。Sci. 400(2008) 230-233]。
An L(2,1)-labeling of a graph G is defined as a function f from the vertex set V(G) into the nonnegative integers such that for any two vertices x, y, |f(x)−f(y)|≥2 if d(x,y)=1 and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) is the distance between x and y in G. The L(2,1)-labeling number λ2,1(G) of G is the smallest number k such that G has an L(2,1)-labeling with k=max{f(x)|x∈V(G)}. In this paper, we consider the graph formed by the skew product and converse skew product of two graphs, and give new upper bounds of the L(2,1)-labeling number, which improves the upper bounds obtained by Shao and Zhang [Z.D. Shao, D. Zhang, Improved upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs, Theoret. Comput. Sci. 400 (2008) 230–233] in many cases.
H.Sakurai：“有机硅化合物的化学。第 2 卷，第 15 章”John Wiley
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