On Geodetic And $k$-Geodetic Sets in Graphs

Bermudo, Sergio; A. Rodriguez-Velazquez, Juan; M.Sigarreta, José; G.Yero, Ismael

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Ars Combinatoria

Volume 096
Pages: 469-478

Research article

On Geodetic And $k$ -Geodetic Sets in Graphs

^¹, ^², ^³, ^²

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

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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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Ars Combinatoria

On Geodetic And $k$ -Geodetic Sets in Graphs

Abstract

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Contents

Ars Combinatoria

On Geodetic And k-Geodetic Sets in Graphs

Abstract

Information

Guidelines

CP Initiatives

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On Geodetic And $k$ -Geodetic Sets in Graphs