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

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