树的罗马控制数和控制数

数学季刊 ›› 2006, Vol. 21 ›› Issue (3): 358-367.

树的罗马控制数和控制数

College of Mathematics and Information Science, Henan University, Kaifeng 475001, China; Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China; Department of Basic Course, Pingdingshan Institute of Technology, Pingdingshan 467000, China

收稿日期:2005-10-11 出版日期:2006-09-30 发布日期:2023-11-28
作者简介:Song Xiao-xin(1973-),male,native of Jiangyan,Jiangsu,Ph.D.,an associate professor of Henan University,engages in graph theory.
基金资助:
Supported by the NSF of education Department of Henan Province(200510475038)；

Roman Domination Number and Domination Number of a Tree

College of Mathematics and Information Science, Henan University, Kaifeng 475001, China; Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China; Department of Basic Course, Pingdingshan Institute of Technology, Pingdingshan 467000, China

Received:2005-10-11 Online:2006-09-30 Published:2023-11-28
About author:Song Xiao-xin(1973-),male,native of Jiangyan,Jiangsu,Ph.D.,an associate professor of Henan University,engages in graph theory.
Supported by:
Supported by the NSF of education Department of Henan Province(200510475038)；

摘要/Abstract

摘要： A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) - 2. The weight of a Roman dominating function is the value . The minimum weight of a Roman dominating function on a graph G, denoted byγR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) =γ(T) + 3.

关键词: Roman dominating function, Roman dominating number, dominating number, healthy spider, wounded spider

Abstract: A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) - 2. The weight of a Roman dominating function is the value . The minimum weight of a Roman dominating function on a graph G, denoted byγR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) =γ(T) + 3.

Key words: Roman dominating function, Roman dominating number, dominating number, healthy spider, wounded spider

中图分类号:

O156

宋晓新, 王晓凤. 树的罗马控制数和控制数[J]. 数学季刊, 2006, 21(3): 358-367.

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