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arXiv · 2412.00574

Asymmetric Colorings of Disjoint Unions of Graphs

Bruno Aguilar·Daibik Barik·Jetharam Bhambhu·Evan Frankel·Nam Hung Tran Nguyen·Revathi Mandava·Aiden Marco·Kyle Pon·Tejas Shende·Yi Wang
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Abstract

The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are disjoint unions of graphs. We will derive a general relationship between the asymmetric coloring number of disjoint copies of graphs and the number of ways to color a single copy asymmetrically, and then look at particular cases such as disjoint copies of paths, stars, cycles, and hypercubes.

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Bruno Aguilar, Daibik Barik, Jetharam Bhambhu, Evan Frankel, Nam Hung Tran Nguyen, Revathi Mandava, Aiden Marco, Kyle Pon, Tejas Shende, Yi Wang. 2024-12-11. Asymmetric Colorings of Disjoint Unions of Graphs. https://arxiv.org/abs/2412.00574

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