Strength based domination in graphs

Document Type : Original paper

Authors

1 Department of Mathematics, Government Engineering College}, Thrissur-680 009, Kerala, India

2 Department of Mathematics, St. Mary's College, Thrissur-680 020, Kerala, India

3 Adjunct Professor, Department of Computer Science and Engineering, Ramco Institute of Technology, Rajapalayam-626117, Tamilnadu, India

Abstract

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.

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References

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Communications in Combinatorics and Optimization
Volume 11, Issue 1
March 2026
Pages 145-154

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