On the Roman domination in the lexicographic product of graphs

Tadeja Kraner Šumenjak (Author), Polona Pavlič (Author), Aleksandra Tepeh (Author)

Abstract

A Roman dominating function of a graph ▫$G = (V,E)$▫ is a function ▫$f \colon V \to \{0,1,2\}$▫ such that every vertex with ▫$f(v) = 0$▫ is adjacent to some vertex with ▫$f(v) = 2$▫. The Roman domination number of ▫$G$▫ is the minimum of ▫$w(f) = \sum_{v \in V}f(v)$▫ over all such functions. Using a new concept of the so-called dominating couple we establish the Roman domination number of the lexicographic product of graphs. We also characterize Roman graphs among the lexicographic product of graphs.

Keywords

teorija grafov;rimska dominacija;popolna dominacija;leksikografski produkt;graph theory;Roman domination;total domination;lexicographic product;

Data

Language:	English
Year of publishing:	2012
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	519.17
COBISS:	3345708
ISSN:	0166-218X
Views:	1121
Downloads:	92
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 2030-2036
Volume:	ǂLetn. ǂ160
Issue:	ǂiss. ǂ13-14
Chronology:	2012
ID:	1471813