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Relation Between k-DRD and Dominating Set

  • S. S. KamathEmail author
  • A. Senthil Thilak
  • Rashmi M
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper, a new parameter on domination is defined by imposing a restriction on the degrees of vertices in the dominating set. For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD-set), if for all u ∈ D there exists a set Cu ⊆ N(u) ∩ (V − D) such that \(|C_u| \leq \lceil \frac {d(u)}{k}\rceil \) and ⋃uDCu = V − D. The minimum cardinality of a k-part degree restricted dominating set of G is called the k-part degree restricted domination number of G and is denoted by \(\gamma _{\frac {d}{k}}(G)\). Here, we determine the k-part degree restricted domination number of some well-known graphs, relation between dominating and k-DRD set, and an algorithm which verifies whether a given dominating set is a k-DRD set or not.

Keywords

Dominating set; Independent dominating set;k-part degree restricted dominating set

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaSurathkal, Srinivasnagar, MangaloreIndia

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