Fractional global domination in graphs

Subramanian Arumugam; Kalimuthu Karuppasamy; Ismail Sahul Hamid

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 1, page 33-44
  • ISSN: 2083-5892

Abstract

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Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, g ( N [ v ] ) = ∑ u ∈ N [ v ] g ( u ) ≥ 1 and g ( N ( v ) ¯ ) = ∑ u ∉ N ( v ) g ( u ) ≥ 1 . A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number γ f g ( G ) is defined as follows: γ f g ( G ) = min|g|:g is an MGDF of G where | g | = ∑ v ∈ V g ( v ) . In this paper we initiate a study of this parameter.

How to cite

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Subramanian Arumugam, Kalimuthu Karuppasamy, and Ismail Sahul Hamid. "Fractional global domination in graphs." Discussiones Mathematicae Graph Theory 30.1 (2010): 33-44. <http://eudml.org/doc/270977>.

@article{SubramanianArumugam2010,
abstract = {Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g(N[v]) = ∑_\{u ∈ N[v]\}g(u) ≥ 1$ and $g(\overline\{N(v)\}) = ∑_\{u ∉ N(v)\}g(u) ≥ 1$. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_\{fg\}(G)$ is defined as follows: $γ_\{fg\}(G)$ = min|g|:g is an MGDF of G where $|g| = ∑_\{v ∈ V\} g(v)$. In this paper we initiate a study of this parameter.},
author = {Subramanian Arumugam, Kalimuthu Karuppasamy, Ismail Sahul Hamid},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; global domination; dominating function; global dominating function; fractional global domination number},
language = {eng},
number = {1},
pages = {33-44},
title = {Fractional global domination in graphs},
url = {http://eudml.org/doc/270977},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Subramanian Arumugam
AU - Kalimuthu Karuppasamy
AU - Ismail Sahul Hamid
TI - Fractional global domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 33
EP - 44
AB - Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g(N[v]) = ∑_{u ∈ N[v]}g(u) ≥ 1$ and $g(\overline{N(v)}) = ∑_{u ∉ N(v)}g(u) ≥ 1$. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_{fg}(G)$ is defined as follows: $γ_{fg}(G)$ = min|g|:g is an MGDF of G where $|g| = ∑_{v ∈ V} g(v)$. In this paper we initiate a study of this parameter.
LA - eng
KW - domination; global domination; dominating function; global dominating function; fractional global domination number
UR - http://eudml.org/doc/270977
ER -

References

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  7. [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc., 1998). Zbl0883.00011
  8. [8] 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
  9. [9] E. Sampathkumar, The global domination number of a graph, J. Math. Phys. Sci. 23 (1989) 377-385. Zbl0729.05045
  10. [10] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory: A Rational Approch to the Theory of Graphs (John Wiley & Sons, New York, 1997). Zbl0891.05003

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