连通控制数与2-连通控制数相等的一类图

数学季刊 ›› 2010, Vol. 25 ›› Issue (1): 98-103.

连通控制数与2-连通控制数相等的一类图

1. School of Mathematics, Shandong University2. College of Information Science and Engineering, Shandong Agriculture University

收稿日期:2006-06-06 出版日期:2010-03-30 发布日期:2023-06-12
作者简介:CHEN Hong-yu(1981- ), female, native of Taian, Shandong, Ph.D., engages in graph theory.

On Graphs with Equal Connected Domination and 2-connected Domination Numbers

1. School of Mathematics, Shandong University2. College of Information Science and Engineering, Shandong Agriculture University

Received:2006-06-06 Online:2010-03-30 Published:2023-06-12
About author:CHEN Hong-yu(1981- ), female, native of Taian, Shandong, Ph.D., engages in graph theory.

摘要/Abstract

摘要： A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components. The k-connected domination number γ_c^k(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G. In this paper, we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.

关键词: connected domination number, 2-connected domination number, trees, unicyclic graphs

Abstract: A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components. The k-connected domination number γ_c^k(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G. In this paper, we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.

Key words: connected domination number, 2-connected domination number, trees, unicyclic graphs

中图分类号:

O157.5

陈宏宇, 朱柘琍. 连通控制数与2-连通控制数相等的一类图[J]. 数学季刊, 2010, 25(1): 98-103.

CHEN Hong-yu, ZHU Zhe-li. On Graphs with Equal Connected Domination and 2-connected Domination Numbers [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(1): 98-103.

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