On the Roman domination in the lexicographic product of graphs

被引：35

作者：

Sumenjak, Tadeja Kraner ^{[2
,3
]}

Pavlic, Polona ^{[3
]}

Tepeh, Aleksandra ^{[1
]}

机构：

[1] Univ Maribor, FEECS, SLO-2000 Maribor, Slovenia

[2] Univ Maribor, FKBV, Hoce 2311, Slovenia

[3] Inst Math Phys & Mech, Ljubljana 1000, Slovenia

来源：

DISCRETE APPLIED MATHEMATICS | 2012年 / 160卷 / 13-14期

关键词：

Roman domination; Total domination; Lexicographic product;

D O I：

10.1016/j.dam.2012.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Roman dominating function of a graph G = (V, E) is a function f : V -> {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) = Sigma(nu is an element of 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. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：2030 / 2036

页数：7

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