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Induced Geodetic Sequence of a Graph | ||
Transactions on Combinatorics | ||
مقاله 4، دوره 14، شماره 3، آذر 2025، صفحه 173-185 اصل مقاله (503.56 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2024.138982.2100 | ||
نویسندگان | ||
Liju Alex Olickal1؛ John Joy Mulloor* 2 | ||
1Department of Mathematics, Bishop Chulaparambil Memorial(BCM) College, Kottayam - 686001 | ||
2Department of Mathematics, Bishop Chulaparambil Memorial(BCM) College, Kottayam, Kerala, India | ||
چکیده | ||
A vertex subset $S$ of a graph $G=(V,E)$ is said to be a geodetic set if every vertex in $G$ is in some $u-v$ geodesic for any $u,v \in S$. The minimum cardinality of such a set is the geodetic number, which is denoted as $g(G)$. In this paper, we introduce the concepts of induced geodetic number and induced geodetic sequence of a graph. We discuss this concept in some graph classes. Also, established the characterization of induced geodetic sequences for trees, unicyclic graphs and cacti. | ||
کلیدواژهها | ||
geodetic sequence؛ geodetic number؛ diameter؛ extreme vertex | ||
مراجع | ||
[1] R. Balakrishnan and K. Ranganathan, A textbook of graph theory, Second edition, Universitext. Springer, New York, 2012. [8] I. M. Peloyo, Geodesic convexity in graphs, Springer, 2013. | ||
آمار تعداد مشاهده مقاله: 89 تعداد دریافت فایل اصل مقاله: 108 |