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Strength based domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 11، شماره 1، خرداد 2026، صفحه 145-154 اصل مقاله (515.55 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29456.2002 | ||
| نویسندگان | ||
| A. Lekha1؛ K.S. Parvathy2؛ S. Arumugam* 3 | ||
| 1Department of Mathematics, Government Engineering College}, Thrissur-680 009, Kerala, India | ||
| 2Department of Mathematics, St. Mary's College, Thrissur-680 020, Kerala, India | ||
| 3Adjunct Professor, Department of Computer Science and Engineering, Ramco Institute of Technology, Rajapalayam-626117, Tamilnadu, India | ||
| چکیده | ||
| Let $G=(V,E)$ be a connected graph. Let $A\subseteq V$ and $v\in V-A.$ The dominating strength of $A$ on $v$ is defined by $s(v,A)=\sum\limits_{u\in A}\frac{1}{d(u,v)}.$ A subset $D$ of $V$ is called a strength based dominating set if for every vertex $v\notin D,$ there exists a subset $A$ of $D$ such that $s(v,A)\geq 1.$ The $sb$-domination number $\gamma_{sb}(G)$ is the minimum cardinality of a strength based dominating set of $G.$ In this paper we initiate a study of this parameter and indicate directions for further research. | ||
| کلیدواژه‌ها | ||
| distance؛ domination؛ dominating strength؛ sb-domination | ||
| مراجع | ||
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[1] G. Chartrand, L. Lesniak, and P. Zhang, Graphs & Digraphs, 6th ed., Chapman & Hall London, New York, 2015.
[2] P. Dankelmann, D. Day, D. Erwin, S. Mukwembi, and H. Swart, Domination with exponential decay, Discrete Math. 309 (2009), no. 19, 5877–5883. https://doi.org/10.1016/j.disc.2008.06.040
[3] Z Gao, Y Shi, C Xi, and J Yue, The extended dominating sets in graphs, Asia-Pacific Journal of Operational Research 40 (2023), no. 5, Article ID: 2340015. https://doi.org/10.1142/S0217595923400158
[4] W. Goddard, M.A. Henning, and C.A. McPillan, The disjunctive domination number of a graph, Quaest. Math. 37 (2014), no. 4, 547–561. https://doi.org/10.2989/16073606.2014.894688
[5] T.W. Haynes, S. Hedetniemi, and P. Slater, Fundamentals of Domination in Graphs, CRC press, Boca Raton, 1998.
[6] M.A. Henning and A. Yeo, Total Domination in Graphs, Springer, New York, 2013. | ||
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