Strong Geodetic Number of Complete Bipartite Graphs and of Graphs with Specified Diameter

被引：14
|
作者：
Irsic, Vesna [1 ,2 ]
机构：
[1] Inst Math Phys & Mech, Ljubljana, Slovenia
[2] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia
来源：
GRAPHS AND COMBINATORICS | 2018年 / 34卷 / 03期
关键词：
Geodetic number; Strong geodetic number; Isometric path number; Complete bipartite graphs; Diameter;
D O I：
10.1007/s00373-018-1885-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The strong geodetic problem is a recent variation of the classical geodetic problem. For a graph G, its strong geodetic number is the cardinality of a smallest vertex subset S, such that each vertex of G lies on one fixed shortest path between a pair of vertices from S. In this paper, some general properties of the strong geodetic problem are studied, especially in connection with the diameter of a graph. The problem is also solved for balanced complete bipartite graphs.
引用
收藏
页码：443 / 456
页数：14
相关论文
共 50 条
  • [1] Strong Geodetic Number of Complete Bipartite Graphs and of Graphs with Specified Diameter
    Vesna Iršič
    Graphs and Combinatorics, 2018, 34 : 443 - 456
  • [2] Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes
    Valentin Gledel
    Vesna Iršič
    Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 2757 - 2767
  • [3] Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes
    Gledel, Valentin
    Irsic, Vesna
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (03) : 2757 - 2767
  • [4] Strong Upper Geodetic Number of Graphs
    Infanta, L. G. Bino
    Xavier, D. Antony
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2021, 12 (03): : 737 - 748
  • [5] Strong Geodetic Number of Graphs and Connectivity
    Wang, Zhao
    Mao, Yaping
    Ge, Huifen
    Magnant, Colton
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (03) : 2443 - 2453
  • [6] Strong Geodetic Number of Graphs and Connectivity
    Zhao Wang
    Yaping Mao
    Huifen Ge
    Colton Magnant
    Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 2443 - 2453
  • [7] THE SPLITTING NUMBER OF COMPLETE BIPARTITE GRAPHS
    JACKSON, B
    RINGEL, G
    ARCHIV DER MATHEMATIK, 1984, 42 (02) : 178 - 184
  • [8] Strong geodetic problem on complete multipartite graphs
    Irsic, Vesna
    Konvalinka, Matjaz
    ARS MATHEMATICA CONTEMPORANEA, 2019, 17 (02) : 481 - 491
  • [9] On the Number of Alternating Paths in Bipartite Complete Graphs
    Patrick Bennett
    Andrzej Dudek
    Elliot Laforge
    Graphs and Combinatorics, 2017, 33 : 307 - 320
  • [10] ON THE BASIS NUMBER OF SOME COMPLETE BIPARTITE GRAPHS
    MCCALL, J
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1985, 31 (03) : 433 - 437
12345