# 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

## Access Full Article

top## Abstract

top## How to cite

topS. 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

top- [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
- [2] E.J. Cockayne, G. Fricke, S.T. Hedetniemi and C.M. Mynhardt, Properties of minimal dominating functions of graphs, Ars Combin. 41 (1995) 107-115. Zbl0840.05090
- [3] G. Chartrand and L. Lesniak, Graphs & Digraphs, Fourth Edition, Chapman & Hall/CRC (2005).
- [4] G.S. Domke, S.T. Hedetniemi and R.C. Laskar, Generalized packings and coverings of graphs, Congr. Numer. 62 (1988) 259-270. Zbl0722.05052
- [5] G.S. Domke, S.T. Hedetniemi and R.C. Laskar, Fractional packings, coverings, and irredundance in graphs, Congr. Numer. 66 (1988) 227-238. Zbl0722.05052
- [6] D.L. Grinstead and P.J. Slater, Fractional domination and fractional packings in graphs, Congr. Numer. 71 (1990) 153-172. Zbl0691.05043
- [7] E.O. Hare, k-weight domination and fractional domination of Pₘ × Pₙ, Congr. Numer. 78 (1990) 71-80.
- [8] J.H. Hattingh, M.A. Henning and J.L. Walters, On the computational complexity of upper distance fractional domination, Australas. J. Combin. 7 (1993) 133-144. Zbl0777.05072
- [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
- [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] 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] 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] 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] D. Vukičević and A. Klobučar, k-dominating sets on linear benzenoids and on the infinite hexagonal grid, Croatica Chemica Acta 80 (2007) 187-191.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.