Abstract
In 1968, Ore determined the maximum size of k-connected graphs with given order and diameter. We give a new short proof.
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References
Ore, O.: Diameters in graphs. J. Combin. Theory 5, 75–81 (1968)
Qiao, P., Zhan, X.: The largest graphs with given order and diameter: a simple proof. Graphs Comb. 35, 1715–1716 (2019)
West, D.B.: Introduction to Graph Theory. Prentice Hall Inc., Upper Saddle River (1996)
Acknowledgements
The author is grateful to Professor Xingzhi Zhan for his constant support and guidance. This research was supported by the NSFC grant 12271170 and Science and Technology Commission of Shanghai Municipality (STCSM) grant 22DZ2229014.
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Zhang, L. A Simple Proof of Ore’s Theorem on the Maximum Size of k-connected Graphs with Given Order and Diameter. Graphs and Combinatorics 39, 33 (2023). https://doi.org/10.1007/s00373-023-02628-w
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DOI: https://doi.org/10.1007/s00373-023-02628-w