Monochromatic connectivity and graph products

Yaping Mao; Zhao Wang; Fengnan Yanling; Chengfu Ye

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arXiv · 1505.01424

Monochromatic connectivity and graph products

Yaping Mao·Zhao Wang·Fengnan Yanling·Chengfu Ye

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Abstract

The concept of monochromatic connectivity was introduced by Caro and Yuster. A path in an edge-colored graph is called a \emph{monochromatic path} if all the edges on the path are colored the same. An edge-coloring of $G$ is a \emph{monochromatic connection coloring} ($MC$-coloring, for short) if there is a monochromatic path joining any two vertices in $G$. The \emph{monochromatic connection number}, denoted by $mc(G)$, is defined to be the maximum number of colors used in an $MC$-coloring of a graph $G$. In this paper, we study the monochromatic connection number on the lexicographical, strong, Cartesian and direct product and present several upper and lower bounds for these products of graphs.

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Yaping Mao, Zhao Wang, Fengnan Yanling, Chengfu Ye. 2015-05-06. Monochromatic connectivity and graph products. https://arxiv.org/abs/1505.01424

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