# Distance in Graphs

Chapter

## 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.

## Keywords

Graph Distance Diameter Radius Steiner distance

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## Notes

### Acknowledgments

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

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## Copyright information

© Springer Science+Business Media, LLC 2011

## Authors and Affiliations

1. 1.School of Computing and Department of Mathematical SciencesClemson UniversityClemsonUSA