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Geodetic Sets in Graphs

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Structural Analysis of Complex Networks

Abstract

Geodetic sets in graphs are briefly surveyed. After an overview of earlier results, we concentrate on recent studies of the geodetic number and related invariants in graphs. Geodetic sets in Cartesian products of graphs and in median graphs are considered in more detail. Algorithmic issues and relations with several other concepts, arising from various convex and interval structures in graphs, are also presented.

MSC2000: Primary 05C12; Secondary 05C99

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Authors and Affiliations

  1. University of Maribor, FEECS, Smetanova 17, 2000, Maribor, Slovenia

    Aleksandra Tepeh

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  1. Boštjan Brešar
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  2. Matjaž Kovše
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  3. Aleksandra Tepeh
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Correspondence to Aleksandra Tepeh .

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  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

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Brešar, B., Kovše, M., Tepeh, A. (2011). Geodetic Sets in Graphs. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_8

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