Distinguishing number and distinguishing index of certain graphs

Saeid Alikhani; Samaneh Soltani

Distinguishing number and distinguishing index of certain graphs

Combinatorics 2016-07-27 v2

Authors: Saeid Alikhani , Samaneh Soltani

Abstract

The distinguishing number (index) $D(G)$ ( $D'(G)$ ) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. In this paper we compute these two parameters for some specific graphs. Also we study the distinguishing number and the distinguishing index of corona product of two graphs.

Keywords

distinguishing number distinguishing index graph vertex labeling edge labeling corona product automorphism

Cite

@article{arxiv.1602.03302,
  title  = {Distinguishing number and distinguishing index of certain graphs},
  author = {Saeid Alikhani and Samaneh Soltani},
  journal= {arXiv preprint arXiv:1602.03302},
  year   = {2016}
}

Comments

15 pages, 6 figures....To appear in FILOMAT

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