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arXiv · 1702.03524

An upper bound on the distinguishing index of graphs with minimum degree at least two

Saeid Alikhani·Samaneh Soltani
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Abstract

The distinguishing index of a simple graph $G$, denoted by $D'(G)$, is the least number of labels in an edge labeling of $G$ not preserved by any non-trivial automorphism. It was conjectured by Pilśniak (2015) that for any 2-connected graph $D'(G) \leq \lceil \sqrt{Δ(G)}\rceil +1$. We prove a more general result for the distinguishing index of graphs with minimum degree at least two from which the conjecture follows. Also we present graphs $G$ for which $D'(G)\leq \lceil \sqrt{Δ}\rceil$.

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Saeid Alikhani, Samaneh Soltani. 2017-02-12. An upper bound on the distinguishing index of graphs with minimum degree at least two. https://arxiv.org/abs/1702.03524

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