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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 427.05042

**Autor: ** Erdös, Paul; Fajtlowicz, Siemion; Hoffman, Alan J.

**Title: ** Maximum degree in graphs of diameter 2. (In English)

**Source: ** Networks 10, 87-90 (1980).

**Review: ** 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.

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C38 Paths and cycles

**Keywords: ** Moore graphs; diameter; maximum degree

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