An upper bound on the distinguishing index of graphs with minimum degree at least two
Author(s):
Article Type:
Research/Original Article (دارای رتبه معتبر)
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 $Delta$, if the minimum degree is at least two, then $ D'(G)leq lceil sqrt{Delta }rceil +1$. We also present graphs $G$ for which $D'(G)leq lceil sqrt{Delta (G)}rceil$.
Keywords:
Language:
English
Published:
Journal of Algebraic Structures and Their Applications, Volume:7 Issue: 2, winter-spring 2020
Pages:
51 to 62
https://www.magiran.com/p2127215
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