On the Total Domination Subdivision Number in Graphs

被引：0
|
作者：
Favaron, O. [1 ,2 ]
Karami, H. [3 ]
Khoeilar, R. [3 ]
Sheikholeslami, S. M. [3 ]
机构：
[1] Univ Paris 11, F-91405 Orsay, France
[2] CNRS, F-91405 Orsay, France
[3] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2014年 / 37卷 / 01期
关键词：
Matching; barrier; total domination number; total domination subdivision number; TOTAL (K)-DOMATIC NUMBER; TOTAL (K)-DOMINATION;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A set S subset of V of vertices in a graph G = (V, E) without isolated vertices is a total dominating set if every vertex of V is adjacent to some vertex in S. The total domination number gamma(t)(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sd(gamma t)(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that sd(gamma t)(G) <= alpha'(G) + 1 for some classes of graphs where alpha'(G) is the maximum cardinality of a matching of G.
引用
下载
收藏
页码：173 / 180
页数：8
相关论文
共 50 条
  • [41] An Upper Bound for the Total Domination Subdivision Number of a Graph
    Karami, H.
    Khoeilar, R.
    Sheikholeslami, S. M.
    Khodkar, A.
    GRAPHS AND COMBINATORICS, 2009, 25 (05) : 727 - 733
  • [42] TOTAL OUTER-CONNECTED DOMINATION SUBDIVISION NUMBERS IN GRAPHS
    Favaron, O.
    Khoeilar, R.
    Sheikholeslami, S. M.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2013, 5 (03)
  • [43] Total domination and total domination subdivision numbers
    Favaron, O.
    Karami, H.
    Sheikholeslami, S. M.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2007, 38 : 229 - 235
  • [44] Lower bounds for the domination number and the total domination number of direct product graphs
    Mekis, Gasper
    DISCRETE MATHEMATICS, 2010, 310 (23) : 3310 - 3317
  • [45] An algorithm to check the equality of total domination number and double of domination number in graphs
    Bahadir, Selim
    TURKISH JOURNAL OF MATHEMATICS, 2020, 44 (05) : 1701 - 1707
  • [46] On a Class of Graphs with Large Total Domination Number
    Bahadir, Selim
    Gozupek, Didem
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2018, 20 (01):
  • [47] Graphs with large total restrained domination number
    Jiang, Hongxing
    Kang, Liying
    Shan, Erfang
    UTILITAS MATHEMATICA, 2010, 81 : 53 - 63
  • [48] Graphs with Large Disjunctive Total Domination Number
    Henning, Michael A.
    Naicker, Viroshan
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2015, 17 (01): : 255 - 282
  • [49] On the total domination number of cross products of graphs
    Ei-Zahar, Mohamed
    Gravier, Sylvain
    Klobucar, Antoaneta
    DISCRETE MATHEMATICS, 2008, 308 (10) : 2025 - 2029
  • [50] FAIR TOTAL DOMINATION NUMBER IN CACTUS GRAPHS
    Hajian, Majid
    Rad, Nader Jafari
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2021, 41 (02) : 647 - 664
12345