Distinguishing Number and Distinguishing Index of Certain Graphs

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 trivial‎‎automorphism‎. ‎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.