Geodesic
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 
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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/

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