Total restrained domination in unicyclic graphs

被引:0
作者
Hattingh, Johannes H. [1 ]
Joubert, Ernst J. [2 ]
Jonck, Elizabeth [2 ]
Plummer, Andrew R. [3 ]
机构
[1] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA
[2] Univ Johannesburg, Dept Math, ZA-2006 Auckland Pk, South Africa
[3] Ohio State Univ, Dept Linguist, Columbus, OH 43210 USA
关键词
Total restrained domination; Unicyclic graph;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let G = (V, E) be a graph. A set S subset of V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V - S is adjacent to a vertex in V - S. The total restrained domination number of G, denoted by gamma(tr)(G), is the minimum cardinality of a total restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then gamma(tr)(U) >= inverted right perpendicularn/2inverted left perpendicular and provide a characterization of graphs achieving this bound.
引用
收藏
页码:81 / 95
页数:15
相关论文
共 14 条
  • [1] Chartrand G., 2005, Graphs and Digraphs, VFourth
  • [2] Cyman J, 2006, AUSTRALAS J COMB, V36, P91
  • [3] Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs
    Hattingh, Johannes H.
    Jonck, Elizabeth
    Joubert, Ernst J.
    Plummer, Andrew R.
    [J]. DISCRETE MATHEMATICS, 2008, 308 (07) : 1080 - 1087
  • [4] Total restrained domination in trees
    Hattingh, Johannes H.
    Jonck, Elizabeth
    Joubert, Ernst J.
    Plummer, Andrew R.
    [J]. DISCRETE MATHEMATICS, 2007, 307 (13) : 1643 - 1650
  • [5] Haynes T.W., 1997, FUNDAMENTALS DOMINAT
  • [6] Haynes T.W., 1998, Chapman & Hall/CRC Pure and Applied Mathematics
  • [7] Total restrained domination in graphs with minimum degree two
    Henning, M. A.
    Maritz, J. E.
    [J]. DISCRETE MATHEMATICS, 2008, 308 (10) : 1909 - 1920
  • [8] Henning M.A., 2006, Quaestiones Mathematicae, V29, P1
  • [9] On total restrained domination in graphs
    Ma, DX
    Chen, XG
    Sun, L
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2005, 55 (01) : 165 - 173
  • [10] Raczek J., 2007, Discussiones Mathematicae Graph Theory, V27, P83, DOI 10.7151/dmgt.1346