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The Total Mutual Visibility Number in Bicyclic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 شهریور 1405 اصل مقاله (457.7 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31659.2919 | ||
| نویسندگان | ||
| Ensieh Golabi Senejani؛ Golam Hossein Fath-Tabar* | ||
| Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran | ||
| چکیده | ||
| Let $G$ be a graph. A subset of vertices $X \subseteq V(G)$ is termed a total mutual-visibility set if, for any pair of vertices $u, v \in V(G)$, one can find a shortest path connecting them such that none of its internal vertices belong to $X$. The cardinality of the largest such set is known as the total mutual-visibility number, denoted by $\mu_t(G)$. In this study, we determine this number for the class of connected bicyclic graphs. Our analysis categorizes these graphs into three structural types based on the connection between their two cycles: disjoint cycles linked by a path, cycles intersecting at a single vertex, and cycles sharing a common path (Theta-graphs). For each category, we establish explicit formulas to calculate the exact value of $\mu_t(G)$. These results cover all structural configurations, including variations in cycle lengths, leaf attachments, and internal vertex arrangements. Ultimately, this work provides a complete characterization of the total mutual-visibility number for bicyclic graphs and sets a foundation for future research. | ||
| کلیدواژه‌ها | ||
| bicyclic graphs؛ mutual-visibility set؛ total mutual-visibility set؛ total mutual- visibility number | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 41 تعداد دریافت فایل اصل مقاله: 67 |
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