距离-本地彩虹连接号

IF 0.5 4区 数学 Q3 MATHEMATICS
F. Septyanto, K. Sugeng
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引用次数: 2

摘要

在边缘着色(不一定是正确的)下,彩虹路径是边缘颜色都不同的路径。d-局部彩虹连接数lrcd(G)(分别为d-局部强彩虹连接数lsrcd(G))是为G的边缘上色所需的最小颜色数,使得任何两个距离不超过d的顶点都可以通过彩虹路径(分别为彩虹测地线)连接起来。这概括了彩虹连接数,即特殊情况d = diam(G)。我们讨论了一些边界和精确值。此外,我们还刻画了所有正整数d, a, b的三元组,使得存在lrcd(G) = a且lsrcd(G) = b的连通图G。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distance-Local Rainbow Connection Number
Abstract Under an edge coloring (not necessarily proper), a rainbow path is a path whose edge colors are all distinct. The d-local rainbow connection number lrcd(G) (respectively, d-local strong rainbow connection number lsrcd(G)) is the smallest number of colors needed to color the edges of G such that any two vertices with distance at most d can be connected by a rainbow path (respectively, rainbow geodesic). This generalizes rainbow connection numbers, which are the special case d = diam(G). We discuss some bounds and exact values. Moreover, we also characterize all triples of positive integers d, a, b such that there is a connected graph G with lrcd(G) = a and lsrcd(G) = b.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
22
审稿时长
53 weeks
期刊介绍: The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.
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