# 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

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topMostafa 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

top- [1] M. Blidia, M. Chellali and L. Volkmann, Some bounds on the p-domination number in trees, submitted for publication. Zbl1100.05069
- [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] 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] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [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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