@article {
author = {Alikhani, S. and Soltani, S.},
title = {THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH},
journal = {Journal of Algebraic Systems},
volume = {8},
number = {2},
pages = {209-217},
year = {2021},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2020.8343.1408},
abstract = {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.},
keywords = {Distinguishing number,distinguishing labeling,determining set},
url = {https://jas.shahroodut.ac.ir/article_1948.html},
eprint = {https://jas.shahroodut.ac.ir/article_1948_8ed554351047fe89af7fd04bb8a07ed1.pdf}
}