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Graphs and Combinatorics

, Volume 34, Issue 3, pp 443–456 | Cite as

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

  • Vesna Iršič
Original Paper

Abstract

The strong geodetic problem is a recent variation of the classical geodetic problem. For a graph G, its strong geodetic number \({{\mathrm{sg}}}(G)\) 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.

Keywords

Geodetic number Strong geodetic number Isometric path number Complete bipartite graphs Diameter 

Mathematics Subject Classification

05C12 05C70 

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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