Elsevier

Discrete Mathematics

Volume 272, Issues 2–3, 6 November 2003, Pages 171-185
Discrete Mathematics

Stratification and domination in graphs

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Abstract

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 γF(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.

MSC

05C69

Keywords

Domination
Stratified graph

Cited by (0)

1

Research supported in part by the University of Natal and the National Research Foundation.

2

Research supported in part by a Western Michigan University Faculty Research and Creative Activities Grant.