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Breaking Symmetry in Graphs by Resolving Sets | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 فروردین 1405 اصل مقاله (417.21 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30820.2632 | ||
| نویسندگان | ||
| Nasrin Soltankhah* 1؛ Meysam Korivand2؛ Sandi Klavžar3 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| 3Faculty of Mathematics and Physics, University of Ljubljana, Slovenia | ||
| چکیده | ||
| Let $dim(G)$ and $D(G)$ respectively denote the metric dimension and the distinguishing number of a graph $G$. It is proved that $D(G) \le dim(G)+1$ holds for every connected graph $G$. Among trees, exactly paths and stars attain the bound, and among connected unicyclic graphs such graphs are $t$-cycles for $t\in \{3,4,5\}$. It is shown that for any $1\leq n< m$, there exists a graph $G$ with $D(G)=n$ and ${\rm dim}(G)=m$. Using the bound $D(G) \le dim(G)+1$, graphs with $D(G) = n(G)-2$ are classified. | ||
| کلیدواژهها | ||
| resolving set؛ metric dimension؛ distinguishing number؛ twin graph؛ almost asymmetric graph | ||
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آمار تعداد مشاهده مقاله: 53 تعداد دریافت فایل اصل مقاله: 25 |
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