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The diameter of random regular graphs

✍ Scribed by Béla Bollobás; W. Fernandez de la Vega

Book ID
110564357
Publisher
Springer-Verlag
Year
1982
Tongue
English
Weight
421 KB
Volume
2
Category
Article
ISSN
0209-9683

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In [1] N.L. Biggs mentions two parameter sets for distance regular graphs that are antipodal covers of a complete graph, for which existence of a corresponding graph was unknown. Here we settle both cases by proving that one does not exist, while there are exactly two nonisomorphic solutions to the

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Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36; 10; 4; 2), but there are 32548 non-isomorphic graphs with parameters (36; 15; 6; 6). (The ÿrst assertion is a special case of a theorem of Sh