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The Largest Graphs with Given Order and Diameter: A Simple Proof

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Abstract

A classic theorem of Ore determines the maximum size of graphs with given order and diameter. We give a very short and simple proof of this result, based on a well-known observation.

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References

  1. Ore, O.: Diameters in graphs. J. Combin. Theory 5, 75–81 (1968)

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  2. West, D.B.: Introduction to Graph Theory. Prentice Hall Inc., Upper Saddle River (1996)

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  3. Zhou, T., Xu, J.M., Liu, J.: Extremal problems on diameter and average distance of graphs. J. Univ. Sci. Tech. China 34(4), 410–413 (2004). (in Chinese)

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Acknowledgements

The authors are grateful to Professor Douglas B. West whose kind and detailed suggestions have simplified an earlier version. This research was supported by the NSFC Grants 11671148 and 11771148 and Science and Technology Commission of Shanghai Municipality (STCSM) Grant 18dz2271000.

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  1. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Pu Qiao & Xingzhi Zhan

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  1. Pu Qiao
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  2. Xingzhi Zhan
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Correspondence to Pu Qiao.

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Qiao, P., Zhan, X. The Largest Graphs with Given Order and Diameter: A Simple Proof. Graphs and Combinatorics 35, 1715–1716 (2019). https://doi.org/10.1007/s00373-019-02098-z

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  • DOI: https://doi.org/10.1007/s00373-019-02098-z

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