Fractional distance domination in graphs

S. Arumugam; Varughese Mathew; K. Karuppasamy

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 3, page 449-459
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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S. Arumugam, Varughese Mathew, and K. Karuppasamy. "Fractional distance domination in graphs." Discussiones Mathematicae Graph Theory 32.3 (2012): 449-459. <http://eudml.org/doc/270889>.

@article{S2012,
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.},
author = {S. Arumugam, Varughese Mathew, K. Karuppasamy},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; distance k-domination; distance k-dominating function; k-packing; fractional distance k-domination; distance -domination; distance -dominating function; -packing; fractional distance -domination},
language = {eng},
number = {3},
pages = {449-459},
title = {Fractional distance domination in graphs},
url = {http://eudml.org/doc/270889},
volume = {32},
year = {2012},
}

TY - JOUR
AU - S. Arumugam
AU - Varughese Mathew
AU - K. Karuppasamy
TI - Fractional distance domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 3
SP - 449
EP - 459
AB - 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.
LA - eng
KW - domination; distance k-domination; distance k-dominating function; k-packing; fractional distance k-domination; distance -domination; distance -dominating function; -packing; fractional distance -domination
UR - http://eudml.org/doc/270889
ER -

References

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  1. [1] S. Arumugam, K. Karuppasamy and I. Sahul Hamid, Fractional global domination in graphs, Discuss. Math. Graph Theory 30 (2010) 33-44, doi: 10.7151/dmgt.1474. Zbl1214.05100
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  9. [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
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  11. [11] S.M. Hedetniemi, S.T. Hedetniemi and T.V. Wimer, Linear time resource allocation algorithms for trees, Technical report URI -014, Department of Mathematics, Clemson University (1987). Zbl0643.68093
  12. [12] A. Meir and J.W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math. 61 (1975) 225-233. Zbl0315.05102
  13. [13] R.R. Rubalcaba, A. Schneider and P.J. Slater, A survey on graphs which have equal domination and closed neighborhood packing numbers, AKCE J. Graphs. Combin. 3 (2006) 93-114. Zbl1121.05088
  14. [14] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory: A Rational Approach to the Theory of Graphs (John Wiley & Sons, New York, 1997). Zbl0891.05003
  15. [15] D. Vukičević and A. Klobučar, k-dominating sets on linear benzenoids and on the infinite hexagonal grid, Croatica Chemica Acta 80 (2007) 187-191. 

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