On stratification and domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 249-272
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A graph G is 2-stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class), where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v. An F-coloring of a graph is a red-blue coloring of the vertices of G in which every blue vertex v belongs to a copy of F rooted at v. The F-domination number γ_F(G) is the minimum number of red vertices in an F-coloring of G. In this paper, we study F-domination, where F is a 2-stratified red-blue-blue path of order 3 rooted at a blue end-vertex. We present characterizations of connected graphs of order n with F-domination number n or 1 and establish several realization results on F-domination number and other domination parameters.
Keywords:
stratified graph, F-domination, domination
@article{DMGT_2006_26_2_a6,
author = {Gera, Ralucca and Zhang, Ping},
title = {On stratification and domination in graphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {249--272},
publisher = {mathdoc},
volume = {26},
number = {2},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/}
}
Gera, Ralucca; Zhang, Ping. On stratification and domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 249-272. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/