Bounds on the Connected Forcing Number of a Graph

被引：9
|
作者：
Davila, Randy [1 ,3 ]
Henning, Michael A. [1 ]
Magnant, Colton [2 ]
Pepper, Ryan [3 ]
机构：
[1] Univ Johannesburg, Dept Pure & Appl Math, ZA-2006 Auckland Pk, South Africa
[2] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30458 USA
[3] Univ Houston Downtown, Dept Math & Stat, Houston, TX 77002 USA
来源：
GRAPHS AND COMBINATORICS | 2018年 / 34卷 / 06期
关键词：
Zero forcing sets; Zero forcing number; Connected dominating sets; Connected domination number; Girth; SPANNING-TREES; ZERO; DOMINATION; SETS; RANK;
D O I：
10.1007/s00373-018-1957-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph. We provide sharp upper and lower bounds on the connected forcing number in terms of the minimum degree, maximum degree, girth, and order of the graph.
引用
收藏
页码：1159 / 1174
页数：16
相关论文
共 50 条
  • [1] Bounds on the Connected Forcing Number of a Graph
    Randy Davila
    Michael A. Henning
    Colton Magnant
    Ryan Pepper
    [J]. Graphs and Combinatorics, 2018, 34 : 1159 - 1174
  • [2] On the forcing connected geodetic number and the connected geodetic number of a graph
    Ahangar, H. Abdollahzadeh
    Fujie-Okamoto, Futaba
    Samodivkin, Vladimir
    [J]. ARS COMBINATORIA, 2016, 126 : 323 - 335
  • [3] The upper connected geodetic number and forcing connected geodetic number of a graph
    Santhakumaran, A. P.
    Titus, P.
    John, J.
    [J]. DISCRETE APPLIED MATHEMATICS, 2009, 157 (07) : 1571 - 1580
  • [4] Bounds on the connected domination number of a graph
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    [J]. DISCRETE APPLIED MATHEMATICS, 2013, 161 (18) : 2925 - 2931
  • [5] Some bounds on the zero forcing number of a graph
    Gentner, Michael
    Rautenbach, Dieter
    [J]. DISCRETE APPLIED MATHEMATICS, 2018, 236 : 203 - 213
  • [6] SPECTRAL BOUNDS FOR THE ZERO FORCING NUMBER OF A GRAPH
    Chen, Hongzhang
    Li, Jianxi
    Xu, Shou-Jun
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2024, 44 (03) : 971 - 982
  • [7] On Tight Bounds for the k-Forcing Number of a Graph
    Zhao, Yan
    Chen, Lily
    Li, Hengzhe
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (02) : 743 - 749
  • [8] On Tight Bounds for the k-Forcing Number of a Graph
    Yan Zhao
    Lily Chen
    Hengzhe Li
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 : 743 - 749
  • [9] Upper bounds on the k-forcing number of a graph
    Amos, David
    Caro, Yair
    Davila, Randy
    Pepper, Ryan
    [J]. DISCRETE APPLIED MATHEMATICS, 2015, 181 : 1 - 10
  • [10] Forcing total outer connected monophonic number of a graph
    Ganesamoorthy, K.
    Priya, S. Lakshmi
    [J]. IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS, 2022, 22 (03): : 278 - 286
12345