## 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.

### MSC:

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

### Keywords:

Moore graphs; diameter; maximum degree
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### 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)
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