## 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 with one fixed blue vertex v specified. We say that F is rooted at v. The F-domination number 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 when (i) F is a 2-stratified path P_{3} on three vertices rooted at a blue vertex which is a vertex of degree 1 in the P _{3} and is adjacent to a blue vertex and with the remaining vertex colored red, and (ii) F is a 2-stratified K_{3} rooted at a blue vertex and with exactly one red vertex.

Original language | English |
---|---|

Pages (from-to) | 203-211 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 286 |

Issue number | 3 |

DOIs | |

Publication status | Published - 28 Sept 2004 |

Externally published | Yes |

## Keywords

- 2-stratified graphs
- Domination
- Trees

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics