DOMINATION NUMBER, INDEPENDENT DOMINATION NUMBER AND 2-INDEPENDENCE NUMBER IN TREES

被引：4

作者：

Dehgardi, Nasrin ^{[1
]}

Sheikholeslami, Seyed Mahmoud ^{[2
]}

Valinavaz, Mina ^{[2
]}

Aram, Hamideh ^{[3
]}

Volkmann, Lutz ^{[4
]}

机构：

[1] Sirjan Univ Technol, Dept Math & Comp Sci, Sirjan, Iran

[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[3] Islamic Azad Univ, Gareziaeddin Ctr, Dept Math, Khoy Branch, Khoy, Iran

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

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2021年 / 41卷 / 01期

关键词：

2-independence number; domination number; independent domination number;

D O I：

10.7151/dmgt.2165

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a graph G, let gamma(G) be the domination number, i(G) be the independent domination number and beta(2)(G) be the 2-independence number. In this paper, we prove that for any tree T of order n >= 2, 4 beta(2)(T) - 3 gamma(T) >= 3i(T), and we characterize all trees attaining equality. Also we prove that for every tree T of order n >= 2, i(T) <= 3 beta(2)(T)/4, and we characterize all extreme trees.

引用

页码：39 / 49

页数：11