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arXiv · 1011.0827

The (strong) rainbow connection numbers of Cayley graphs of Abelian groups

Hengzhe Li·Xueliang Li·Sujuan Liu
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Abstract

A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $i$ for which there exists an $i$-edge-coloring of $G$ such that every two distinct vertices of $G$ are connected by a rainbow path. The strong rainbow connection number $src(G)$ of $G$ is the minimum integer $i$ for which there exists an $i$-edge-coloring of $G$ such that every two distinct vertices $u$ and $v$ of $G$ are connected by a rainbow path of length $d(u,v)$. In this paper, we give upper and lower bounds of the (strong) rainbow connection Cayley graphs of Abelian groups. Moreover, we determine the (strong) rainbow connection numbers of some special cases.

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Hengzhe Li, Xueliang Li, Sujuan Liu. 2010-11-03. The (strong) rainbow connection numbers of Cayley graphs of Abelian groups. https://arxiv.org/abs/1011.0827

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