Critical graphs with Roman domination number four

被引：0

作者：

Martinez-Perez, A. ^{[1
]}

Oliveros, D. ^{[2
]}

机构：

[1] Fac CC Soci Talavera, Avda Real Fabrica de Seda S-N, Toledo 45600, Spain

[2] Univ Nacl Autonoma Mexico, Inst Math, Mexico City, DF, Mexico

来源：

AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS | 2020年 / 17卷 / 03期

关键词：

Roman domination; critical; 05C69;

D O I：

10.1016/j.akcej.2019.12.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Roman domination function on a graph G is a function r:V(G)-> {0,1,2} satisfying the condition that every vertex u for which r(u) = 0 is adjacent to at least one vertex v for which r(v) = 2. The weight of a Roman domination function is the value r(V(G))=<mml:munder>Sigma u is an element of V(G)</mml:munder>r(u). The Roman domination number gamma R(G) of G is the minimum weight of a Roman domination function on G. "Roman Criticality" often refers to the study of graphs where the Roman domination number decreases when adding an edge or removing a vertex of the graph. In this paper we add some condition to this notion of criticality and give a complete characterization of critical graphs with Roman Domination number gamma R(G)=4.

引用

页码：804 / 809

页数：6