On the p-domination number of cactus graphs

@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 -