Stratification and Domination in Graphs
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.) We color the vertices in one color class red and the other color class blue. Let F be a 2-stratified graph rooted at some blue vertex v. The F-domination number γ F(G) of a graph G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that every blue vertex v of G belongs to a copy of F rooted at v. In this paper we investigate the F-domination number for all 2-stratified graphs F of order n≤3 rooted at a blue vertex.
Chartrand, Gary; Haynes, Teresa W.; Henning, Michael A.; and Zhang, Ping. 2003. Stratification and Domination in Graphs. Discrete Mathematics. Vol.272(2-3). 171-185. https://doi.org/10.1016/S0012-365X(03)00078-5 ISSN: 0012-365X