%0 Journal Article
%T THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Alikhani, S.
%A Soltani, S.
%D 2021
%\ 01/01/2021
%V 8
%N 2
%P 209-217
%! THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH
%K Distinguishing number
%K distinguishing labeling
%K determining set
%R 10.22044/jas.2020.8343.1408
%X The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is called the cost of $d$-distinguishing $G$ and is denoted by $\rho_d(G)$. A set of vertices $S\subseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of $G$, ${\rm Det}(G)$, is the minimum cardinality of determining sets of $G$. In this paper we compute the cost and the determining number for the friendship graphs and corona product of two graphs.
%U https://jas.shahroodut.ac.ir/article_1948_8ed554351047fe89af7fd04bb8a07ed1.pdf