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

  • Pu QiaoEmail author
  • Xingzhi Zhan
Original Paper


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.


Diameter Size Extremal graphs 



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.


  1. 1.
    Ore, O.: Diameters in graphs. J. Combin. Theory 5, 75–81 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    West, D.B.: Introduction to Graph Theory. Prentice Hall Inc., Upper Saddle River (1996)zbMATHGoogle Scholar
  3. 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) MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina

Personalised recommendations