Characterization of Roman domination critical unicyclic graphs

被引：0

作者：

Hansberg, A. ^{[1
]}

Rad, N. Jafari ^{[2
]}

Volkmann, L. ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Lehrstuhl Math 2, D-52056 Aachen, Germany

[2] Shahrood Univ Technol, Dept Math, Shahrood, Iran

来源：

UTILITAS MATHEMATICA | 2011年 / 86卷

关键词：

Domination; Roman domination; Roman domination critical graph; unicyclic graph;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Roman dominating function on a graph G is a function f : V(G) -> {0, 1, 2} satisfying the condition that every vertex u of G for which f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2. The weight of a Roman dominating function is the value f(V(G)) = Sigma(u is an element of V(G)) f(u). The Roman domination number, gamma(R)(G), of G is the minimum weight of a Roman dominating function on G. A graph G is said to be Roman domination vertex critical or just gamma(R)-vertex critical, if gamma(R)(G - v) < gamma(R)(G) for any vertex v is an element of V(G). Similarly, G is Roman domination edge critical or just gamma(R)-edge critical, if gamma(R)(G + e) < gamma(R)(G) for any edge e is not an element of E(G). In this paper, we characterize gamma(R)-vertex critical connected unicyclic graphs as well gamma(R)-edge critical connected unicyclic graphs.

引用

页码：129 / 146

页数：18