Title of article
An upper bound on the distinguishing index of graphs with minimum degree at least two
Author/Authors
Alikhani, Saeid Department of Mathematics - Yazd University, Yazd, Iran , Soltani, Samaneh Department of Mathematics - Yazd University, Yazd, Iran
Pages
12
From page
51
To page
62
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. We prove that for a connected graph G with maximum degree Δ, if the minimum degree is at least two, then D′(G)≤⌈Δ−−√⌉+1. We also present graphs G for which D′(G)≤⌈Δ(G)−−−−−√⌉.
Keywords
distinguishing index , edge-colourings , upper bound
Journal title
Journal of Algebraic Structures and Their Applications
Serial Year
2020
Record number
2605284
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