The number of distinguishing colorings of a Cartesian product graph

Abstract

A vertex coloring is called distinguishing if the identity is the only automorphism that can preserve it. The distinguishing threshold $\theta (G)$ of a graph $G$ is the minimum number of colors $k$ required that any arbitrary $k$-coloring of $G$ is distinguishing. In this paper, we calculate the distinguishing threshold of a Cartesian product graph. Moreover, we calculate the number of non-equivalent distinguishing colorings of grids.

11 pages, 4 figures

References in corpus (4)

• Number of Distinguishing Colorings and Partitions
• Distinguishing threshold of graphs
• The Cost of Edge-distinguishing of the Cartesian Product of Connected Graphs
• Distinguishing threshold for some graph operations