Erdős, Paul; Fajtlowicz, Siemion; Hoffman, Alan J. Maximum degree in graphs of diameter 2. (English) Zbl 0427.05042 Networks 10, 87-90 (1980). 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. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 28 Documents MSC: 05C35 Extremal problems in graph theory 05C38 Paths and cycles Keywords:Moore graphs; diameter; maximum degree PDFBibTeX XMLCite \textit{P. Erdős} et al., Networks 10, 87--90 (1980; Zbl 0427.05042) Full Text: DOI References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.