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Distance in Graphs

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Structural Analysis of Complex Networks

Abstract

The distance between two vertices is the basis of the definition of several graph parameters including diameter, radius, average distance and metric dimension. These invariants are examined, especially how they relate to one another and to other graph invariants and their behaviour in certain graph classes. We also discuss characterizations of graph classes described in terms of distance or shortest paths. Finally, generalizations are considered.

MSC2000: Primary 05C12; Secondary 05C20, 05C38

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Acknowledgments

We would like to thank Peter Dankelmann for sharing his thoughts on average distance with us.

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Authors and Affiliations

  1. School of Computing and Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-1906, USA

    Wayne Goddard

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  1. Wayne Goddard
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  2. Ortrud R. Oellermann
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Correspondence to Wayne Goddard .

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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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Goddard, W., Oellermann, O.R. (2011). Distance in Graphs. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_3

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