Trees with distinguishing number two

Saeid Alikhani; Samaneh Soltani

Trees with distinguishing number two

Combinatorics 2016-11-29 v1

Authors: Saeid Alikhani , Samaneh Soltani

Abstract

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. In this paper we characterize all trees with radius at most three and distinguishing number two. Also we present a necessary condition for trees with distinguishing number two and radius more than three.

Keywords

trees graph pebbling graph theory

Cite

@article{arxiv.1611.09291,
  title  = {Trees with distinguishing number two},
  author = {Saeid Alikhani and Samaneh Soltani},
  journal= {arXiv preprint arXiv:1611.09291},
  year   = {2016}
}

Comments

6 pages, 2 figures

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