Contents

Ars Combinatoria

  • Research article

On Geodetic And \(k\)-Geodetic Sets in Graphs

Sergio Bermudo1, Juan A. Rodriguez-Velazquez2, José M.Sigarreta3, Ismael G.Yero2
1Department of Economy, Quantitative Methods and Economic History Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, Spain
2Department of Computer Engineering and Mathematics Rovira i Virgili University, Av. Paisos Catalans 26, 43007 Tarragona, Spain.
3Faculty of Mathematics, Autonomous University of Guerrero Carlos E. Adame 5, Col. La Garita, Acapulco, Guerrero, Mexico
  • Published: 31/07/2010

Abstract

We investigate the relationship between geodetic sets, \(k\)-geodetic sets, dominating sets, and independent sets in arbitrary graphs. As a consequence of the study, we provide several tight bounds on the geodetic number of a graph.

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Citation
Sergio Bermudo, Juan A. Rodriguez-Velazquez, José M.Sigarreta, Ismael G.Yero. On Geodetic And \(k\)-Geodetic Sets in Graphs[J], Ars Combinatoria, Volume 096. 469-478. .