Strength based domination in graphs

Articles in Press

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 Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India

Abstract

Let G=(V,E) be a connected graph. Let A⊆V and v∈V−A. The dominating strength of A on v is defined by s(v,A)=∑u∈A1d(u,v). A subset D of V is called a strength based dominating set if for every vertex v∉D, there exists a subset A of D such that s(v,A)≥1. The sb-domination number γsb(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

Articles in Press, Accepted Manuscript
Available Online from 05 June 2024

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