关于树图中全控制数与全外部连通控制数比值的研究

庄蔚

doi:10.13568/j.cnki.651094.651316.2020.05.26.0005

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关于树图中全控制数与全外部连通控制数比值的研究

更新时间：2026-01-21

- 关于树图中全控制数与全外部连通控制数比值的研究
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 38, Issue 3, Pages: 269-274(2021)
- 作者机构：
  
  厦门理工学院应用数学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2020.05.26.0005
  CLC： O157.5
- Published：2021
- 稿件说明：
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[1]庄蔚.关于树图中全控制数与全外部连通控制数比值的研究[J].新疆大学学报(自然科学版)(中英文),2021,38(03):269-274.
[1]庄蔚.关于树图中全控制数与全外部连通控制数比值的研究[J].新疆大学学报(自然科学版)(中英文),2021,38(03):269-274. DOI： 10.13568/j.cnki.651094.651316.2020.05.26.0005.

DOI：10.13568/j.cnki.651094.651316.2020.05.26.0005.

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.

Abstract

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.

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references

HENNING M A.A survey of selected recent results on total domination in graphs[J].Discrete Mathematics,2009,309:32-63.

CYMAN J.Total outer-connected domination in trees[J].Discussiones Mathematicae Graph Theory,2010,30:377-383.

SHAN E F,KANG L,HENNING M A.A characterization of trees with equal total domination and paired-domination numbers[J].Australasian Journal of Combinatorics,2004,30:31-39.

FAVARON O,KARAMI H,SHEKHOLESLAMI S M.On the total outer-connected domination in graphs[J].Journal of Combinatorial Optimization,2014,27:451-461.

CYMAN J,RACZEK J.Total outer-connected domination numb ers of trees[J].Discrete Applied Mathematics,2009,157:3198-3202.

DORFLING M,GODDARD W,HENNING M A,et al.Construction of trees and graphs with equal domination parameters[J].Discrete Mathematics,2006,306:2647-2654.

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