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