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

被引：16

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

页码：443 / 456

页数：14

共 50 条

[31] Strong Edge Geodetic Problem on Complete Multipartite Graphs and Some Extremal Graphs for the Problem
Sandi Klavžar
Eva Zmazek
Bulletin of the Iranian Mathematical Society, 2024, 50
[32] Strong Edge Geodetic Problem on Complete Multipartite Graphs and Some Extremal Graphs for the Problem
Klavzar, Sandi
Zmazek, Eva
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2024, 50 (01)
[33] Complete bipartite factorisations by complete bipartite graphs
Martin, N
DISCRETE MATHEMATICS, 1997, 167 : 461 - 480
[34] Complete bipartite factorisations by complete bipartite graphs
Martin, N.
Discrete Mathematics, 1997, 167-168 : 461 - 480
[35] HOMOMORPHISMS OF INFINITE BIPARTITE GRAPHS ONTO COMPLETE BIPARTITE GRAPHS
ZELINKA, B
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1983, 33 (04) : 545 - 547
[36] Diameter of the NEPS of bipartite graphs
Brualdi, RA
Shen, J
DISCRETE MATHEMATICS, 2001, 226 (1-3) : 373 - 376
[37] SIZE RAMSEY NUMBER OF BIPARTITE GRAPHS AND BIPARTITE RAMANUJAN GRAPHS
Javadi, R.
Khoeini, F.
TRANSACTIONS ON COMBINATORICS, 2019, 8 (02) : 45 - 51
[38] Random Dense Bipartite Graphs and Directed Graphs With Specified Degrees
Greenhill, Catherine
McKay, Brendan D.
RANDOM STRUCTURES & ALGORITHMS, 2009, 35 (02) : 222 - 249
[39] The competition graphs of oriented complete bipartite graphs
Kim, Suh-Ryung
Lee, Jung Yeun
Park, Boram
Sano, Yoshio
DISCRETE APPLIED MATHEMATICS, 2016, 201 : 182 - 190
[40] Complete Graphs and Bipartite Graphs in a Random Graph
Feng, Lijin
Barr, Jackson
2021 5TH INTERNATIONAL CONFERENCE ON VISION, IMAGE AND SIGNAL PROCESSING (ICVISP 2021), 2021, : 259 - 266

← 1 2 3 4 5 →