Maximum degree in graphs of diameter 2. (English) Zbl 0427.05042

Summary: It is well known that there are at most four Moore graphs of diameter 2, i.e., graphs of diameter 2, maximum degree d, and \(d^2+1\) vertices. The purpose of this paper is to prove that with the exception of \(C_4\), there are no graphs of diameter 2, of maximum degree d, and with \(d^2\) vertices.


05C35 Extremal problems in graph theory
05C38 Paths and cycles
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