# On the p-domination number of cactus graphs

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

top

## Abstract

top
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

top

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

top
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

## NotesEmbed?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.