The diameter of total domination and independent domination vertex-critical graphs

被引：0
|
作者：
Edwards, M. [1 ]
MacGillivray, G. [1 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
来源：
AUSTRALASIAN JOURNAL OF COMBINATORICS | 2012年 / 52卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the diameter of a total domination vertex-critical graph is at most 5(gamma(t) - 1)/3, and that the diameter of an independent domination vertex- critical graph is at most 2(i- 1). For all values of gamma(t) equivalent to 2 (mod 3) there exists a total domination vertex- critical graph with the maximum possible diameter. For all values of i >= 2 there exists an independent domination vertex-critical graph with the maximum possible diameter.
引用
收藏
页码：33 / 39
页数：7
相关论文
共 50 条
  • [21] VERTEX DOMINATION-CRITICAL GRAPHS
    FULMAN, J
    HANSON, D
    MACGILLIVRAY, G
    NETWORKS, 1995, 25 (02) : 41 - 43
  • [22] Paired Domination Vertex Critical Graphs
    Xinmin Hou
    Michelle Edwards
    Graphs and Combinatorics, 2008, 24 : 453 - 459
  • [23] Paired Domination Vertex Critical Graphs
    Hou, Xinmin
    Edwards, Michelle
    GRAPHS AND COMBINATORICS, 2008, 24 (05) : 453 - 459
  • [24] Domination critical graphs with higher independent domination numbers
    Ao, S
    Cockayne, EJ
    MacGillivray, G
    Mynhardt, CM
    JOURNAL OF GRAPH THEORY, 1996, 22 (01) : 9 - 14
  • [25] The maximum diameter of total domination edge-critical graphs
    Henning, Michael A.
    van der Merwe, Lucas C.
    DISCRETE MATHEMATICS, 2012, 312 (02) : 397 - 404
  • [26] Total Domination in Graphs with Diameter 2
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    Yeo, Anders
    JOURNAL OF GRAPH THEORY, 2014, 75 (01) : 91 - 103
  • [27] Critical graphs with respect to total domination and connected domination
    Kaemawichanurat, P.
    Caccetta, L.
    Ananchuen, N.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2016, 65 : 1 - 13
  • [28] THE DIAMETER OF EDGE DOMINATION CRITICAL GRAPHS
    PARIS, M
    NETWORKS, 1994, 24 (04) : 261 - 262
  • [29] A note on independent vertex edge domination in graphs
    Chen, Xue-gang
    Yin, Kai
    Gao, Ting
    DISCRETE OPTIMIZATION, 2017, 25 : 1 - 5
  • [30] The Diameter of Connected Domination Critical Graphs
    Zhao Chengye
    Cao Feilong
    ARS COMBINATORIA, 2012, 107 : 537 - 541
12345