Roman domination in graphs

被引:447
|
作者
Cockayne, EJ
Dreyer, PA [1 ]
Hedetniemi, SM
Hedetniemi, ST
机构
[1] RAND Corp, Santa Monica, CA 90407 USA
[2] Univ Victoria, Victoria, BC V8W 3P4, Canada
[3] Clemson Univ, Clemson, SC 29634 USA
基金
加拿大自然科学与工程研究理事会;
关键词
graph theory; domination; facilities location;
D O I
10.1016/j.disc.2003.06.004
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A Roman dominating function on a graph G = (V, E) is a function f : V --> f{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = E,,,, f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper, we study the graph theoretic properties of this variant of the domination number of a graph. (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码:11 / 22
页数:12
相关论文
共 50 条
  • [1] Roman domination in graphs
    University of Victoria, Victoria, BC, V8W 3P4, Canada
    不详
    不详
    [J]. 1600, 11-22 (March 6, 2004):
  • [2] Roman and inverse Roman domination in graphs
    Zaman, Zulfiqar
    Kumar, M. Kamal
    Ahmad, Saad Salman
    [J]. NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2018, 24 (03) : 142 - 150
  • [3] Complexity of Roman {2}-domination and the double Roman domination in graphs
    Padamutham, Chakradhar
    Palagiri, Venkata Subba Reddy
    [J]. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (03) : 1081 - 1086
  • [4] Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs
    Cabrera Martinez, A.
    Garcia-Gomez, C.
    Rodriguez-Velazquez, J. A.
    [J]. FUNDAMENTA INFORMATICAE, 2022, 185 (03) : 201 - 220
  • [5] Signed Roman domination in graphs
    Ahangar, H. Abdollahzadeh
    Henning, Michael A.
    Loewenstein, Christian
    Zhao, Yancai
    Samodivkin, Vladimir
    [J]. JOURNAL OF COMBINATORIAL OPTIMIZATION, 2014, 27 (02) : 241 - 255
  • [6] Roman domination in signed graphs
    Joseph, James
    Joseph, Mayamma
    [J]. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2023, 8 (02) : 349 - 358
  • [7] Global Roman domination in graphs
    Pushpam, P. Roushini Leely
    Padmapriea, S.
    [J]. DISCRETE APPLIED MATHEMATICS, 2016, 200 : 176 - 185
  • [8] TOTAL ROMAN DOMINATION IN GRAPHS
    Ahangar, Hossein Abdollahzadeh
    Henning, Michael A.
    Samodivkin, Vladimir
    Yero, Ismael G.
    [J]. APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2016, 10 (02) : 501 - 517
  • [9] Signed Roman -Domination in Graphs
    Henning, Michael A.
    Volkmann, Lutz
    [J]. GRAPHS AND COMBINATORICS, 2016, 32 (01) : 175 - 190
  • [10] ON THE ROMAN DOMINATION STABLE GRAPHS
    Hajian, Majid
    Rad, Nader Jafari
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2017, 37 (04) : 859 - 871