图中的支配子半强颜色划分

IF 0.7 Q2 MATHEMATICS
Praba Venkatrengan, Swaminathan Venkatasubramanian, R. Sundareswaran
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引用次数: 0

摘要

设GG=(V,E)(V,E)是一个简单图。如果对于vv中的每个顶点vv,|N(v)x_ S|≤1|N(v)x_ S|≤1,或者SS的两个顶点在vv中没有相同的邻居,也就是说,没有两个SS的顶点通过vv中长度为2的路径连接,则称子集SS是半强的。GG的半强分区的最小基数称为GG的半强色数,用χsG表示。如果每个顶点都支配某个颜色类,即每个顶点都与某个颜色类别的每个元素相邻,则一个适当的颜色分区称为支配者颜色分区。本文考虑半强色分划,而不是适当的色分划。获得了几个有趣的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dominator semi strong color partition in graphs
Let GG =(V,E)(V,E) be a simple graph. A subset SS is said to be Semi-Strong if for every vertex vv in VV, |N(v)∩S|≤1|N(v)∩S|≤1, or no two vertices of SS have the same neighbour in VV, that is, no two vertices of SS are joined by a path of length two in VV. The minimum cardinality of a semi-strong partition of GG is called the semi-strong chromatic number of GG and is denoted by χsGχsG. A proper colour partition is called a dominator colour partition if every vertex dominates some colour class, that is , every vertex is adjacent with every element of some colour class. In this paper, instead of proper colour partition, semi-strong colour partition is considered and every vertex is adjacent to some class of the semi-strong colour partition.Several interesting results are obtained.
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