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Arc-distinguishing of orientations of graphs
[Submitted on 25 Feb 2024 (v1), last revised 10 Sep 2026 (this v · 2024-02-26 · via math updates on arXiv.org

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Abstract:The distinguishing index $D'(G)$ of a graph $G$ is the minimum number of colours in an edge colouring preserved only by the identity automorphism. We study how orienting the edges affects this parameter, relating the minimum and maximum distinguishing indices over all orientations of $G$ to $D'(G)$. We establish bounds and exact relations for bipartite graphs and trees, and study rigid orientations of traceable and claw-free graphs. Our results answer a question of Meslem and Sopena on unbalanced complete bipartite graphs.

Submission history

From: Jakub Kwaśny [view email]
[v1] Sun, 25 Feb 2024 18:33:36 UTC (10 KB)
[v2] Thu, 10 Sep 2026 14:17:45 UTC (11 KB)