DMGT

Discussiones Mathematicae Graph Theory 26(2) (2006) 249-272
DOI: https://doi.org/10.7151/dmgt.1317

ON STRATIFICATION AND DOMINATION IN GRAPHS

Ralucca Gera

Department of Applied Mathematics
Naval Postgradute School
Monterey, CA 93943-5216, USA
e-mail: RGera@nps.edu

Ping Zhang

Department of Mathematics
Western Michigan University
Kalamazoo, MI 49008, USA
e-mail: ping.zhang@wmich.edu

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), 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.

2000 Mathematics Subject Classification: 05C15, 05C69.

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Received 31 August 2005
Revised 31 March 2006