关于树图中全控制数与全外部连通控制数比值的研究  

Total Domination Versus Total Outer Connected Domination in Trees

作　　者：庄蔚 ZHUANG Wei(School of Applied Mathematics,Xiamen University of Technology,Xiamen Fujian 361024,China)

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《新疆大学学报（自然科学版）（中英文）》2021年第3期269-274,共6页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：福建省自然科学基金青年项目(2015J05017).

摘　　要：1980年Cockayne等人提出全控制数γt(G),目前已成为最重要的控制参数之一.近些年,一种与全控制数密切相关的控制参数被广泛研究,即:全外部连通控制数γtc(G).众所周知,γt(G)≤γtc(G).在本文中,我们证明了若T没有强支撑点,则γtc(T)≤5γt(T)/2-2.同时,我们也刻画出了达到这个不等式上界的极图.Total domination number γt(G), is one of the most important domination parameters, which was introduced by Cockayne et al. in 1980. In recent years, a variant of total domination number have been extensively studied, namely, total outer connected domination number γtc(G). It is well known that γt(G) ≤ γtc(G). In this paper, we show that if T has no strong support vertex, we have that γtc(T) ≤5γt(T)/2-2. In addition, we provide a constructive characterizations of the trees achieving equality in the bound.

关 键 词：全控制 全外部连通控制 树图 

分 类 号：O157.5[理学—数学]