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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1288,
author = {Mostafa Blidia and Mustapha Chellali and Lutz Volkmann},
title = {On the p-domination number of cactus graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {355-361},
zbl = {1121.05083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1288}
}
Mostafa Blidia; Mustapha Chellali; Lutz Volkmann. On the p-domination number of cactus graphs. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 355-361. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1288/
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