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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
Full Text: DOI
[1] ”On graphs that do not contain a Thompsen graph,” Can. Math. Bull., v.g. 281–285 (1966). · Zbl 0178.27302
[2] and , ”Domination in graphs of diameter 2,” in preparation.
[3] Erdös, Publ. Math. Inst. Hung. Acad. Sci. 7/A pp 623– (1962)
[4] Hoffman, IBM J. Res. Dev. 4 pp 497– (1960)
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