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Discussiones Mathematicae Graph Theory 32(3) (2012) 449-459
DOI: https://doi.org/10.7151/dmgt.1609

Fractional Distance Domination in Graphs

S. Arumugam1,2, Varughese Mathew3 and K. Karuppasamy1 1National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH)

Abstract

Let G = (V,E) be a connected graph and let k be a positive integer with k ≤ rad(G). A subset D ⊆ V is called a distance k-dominating set of G if for every v ∈ V −D, there exists a vertex u ∈ D such that d(u,v) ≤ k. In this paper we study the fractional version of distance k-domination and related parameters.

Keywords: domination, distance k-domination, distance k-dominating
function, k-packing, fractional distance k-domination

2010 Mathematics Subject Classification: 05C69, 05C72.

References

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Received 22 December 2010
Revised 12 August 2011
Accepted 16 August 2011