The largest graphs with given order and diameter: A simple proof
Pu Qiao, Xingzhi Zhan
TL;DR
This paper provides a concise and straightforward proof for identifying the largest graphs with a specified number of vertices and diameter, building on Ore's theorem.
Contribution
It offers a simplified proof of the maximal graphs with given order and diameter, enhancing understanding and accessibility of the original result.
Findings
Identifies the largest graphs with given order and diameter
Provides a shorter, elementary proof of a known theorem
Clarifies the structure of extremal graphs
Abstract
A consequence of Ore's classic theorem characterizing the maximal graphs with given order and diameter is a determination of the largest such graphs. We give a very short and simple proof of this smaller result, based on a well-known elementary observation.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory