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Random strongly regular graphs?

✍ Scribed by Peter J. Cameron

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 203 KB
Volume: 10
Category: Article
ISSN: 1571-0653
DOI: 10.1016/s1571-0653(04)00358-0

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📜 SIMILAR VOLUMES

✍ Peter J. Cameron 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 289 KB

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

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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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The concept of strongly balanced graph is introduced. It is shown that there exists a strongly balanced graph with u vertices and e edges if and only if I s u -1 s e s ( 2 " ) . This result is applied to a classic question of Erdos and Renyi: What is the probability that a random graph on n vertices

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In this paper we solve 3 of the 6 problems of A. Kotzig on regular and strongly-regular self-complementary graphs, mentioned in "Graph Theory and Related Topics" edited by J.A.