THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH | ||
| Journal of Algebraic Systems | ||
| دوره 8، شماره 2، فروردین 2021، صفحه 209-217 اصل مقاله (356.56 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2020.8343.1408 | ||
| نویسندگان | ||
| S. Alikhani* 1؛ S. Soltani2 | ||
| 1Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. | ||
| 2Department of Mathematics, Yazd University, 89195-741, Yazd, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Distinguishing number؛ distinguishing labeling؛ determining set | ||
|
آمار تعداد مشاهده مقاله: 480 تعداد دریافت فایل اصل مقاله: 495 |
||