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## Discussiones Mathematicae Graph Theory

2012 | 32 | 3 | 449-459
Tytuł artykułu

### Fractional distance domination in graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
449-459
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-12-22
poprawiono
2011-08-12
zaakceptowano
2011-08-16
Twórcy
autor
• National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626 126, India
• School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia
autor
• Department of Mathematics, Mar Thoma College, Tiruvalla-689 103, India
autor
• National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626 126, India
Bibliografia
• [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.
• [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.
• [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.
• [5] G.S. Domke, S.T. Hedetniemi and R.C. Laskar, Fractional packings, coverings, and irredundance in graphs, Congr. Numer. 66 (1988) 227-238.
• [6] D.L. Grinstead and P.J. Slater, Fractional domination and fractional packings in graphs, Congr. Numer. 71 (1990) 153-172.
• [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.
• [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in graphs: Advanced Topics (Marcel Dekker, New York, 1998).
• [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).
• [12] A. Meir and J.W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math. 61 (1975) 225-233.
• [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.
• [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).
• [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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Bibliografia
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