On the p-domination number of cactus graphs

Mostafa Blidia; Mustapha Chellali; Lutz Volkmann

Discussiones Mathematicae Graph Theory (2005)

  • Volume: 25, Issue: 3, page 355-361
  • ISSN: 2083-5892

Abstract

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Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.

How to cite

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Mostafa Blidia, Mustapha Chellali, and Lutz Volkmann. "On the p-domination number of cactus graphs." Discussiones Mathematicae Graph Theory 25.3 (2005): 355-361. <http://eudml.org/doc/270407>.

@article{MostafaBlidia2005,
abstract = {Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.},
author = {Mostafa Blidia, Mustapha Chellali, Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {p-domination number; cactus graphs; -domination number; Cactus graph},
language = {eng},
number = {3},
pages = {355-361},
title = {On the p-domination number of cactus graphs},
url = {http://eudml.org/doc/270407},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Mostafa Blidia
AU - Mustapha Chellali
AU - Lutz Volkmann
TI - On the p-domination number of cactus graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 3
SP - 355
EP - 361
AB - Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.
LA - eng
KW - p-domination number; cactus graphs; -domination number; Cactus graph
UR - http://eudml.org/doc/270407
ER -

References

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  1. [1] M. Blidia, M. Chellali and L. Volkmann, Some bounds on the p-domination number in trees, submitted for publication. Zbl1100.05069
  2. [2] J.F. Fink and M.S. Jacobson, n-domination in graphs, in: Y. Alavi and A.J. Schwenk, eds, Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1985) 283-300. Zbl0573.05049
  3. [3] J.F. Fink and M.S. Jacobson, On n-domination, n-dependence and forbidden subgraphs, in: Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1985) 301-312. 
  4. [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  5. [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011

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