Combinatorics and Graph Theory

    

On Conway's 99-graph: Parts 1-20

Authors: E. Guseinov

This preprint in Russian reflects some of my results on Conway's 99-graph (G) obtained in 2022-2023 during a research that I did on my own. Here I prove that G is Cartesian indecomposable (Part 10, Theorem 36), G can not be obtained by a group-theoretic generalization of Berlekamp-Seidel's construction (Part 11), G contains no Hamming graph H(4,3) (Part 8, Theorem 28), G is not contained in strongly regular graphs srg(243,22,1,2) (Part 12, Theorem 40), the independence number of G is at least 10 (Part 4, Theorem 21). Parts 12-17, 19 and 20 reflect attempts to prove G may contain H(2,3), i. e. the Paley graph P(9). I'm currently accepting offers to join a graph theoretical research, so you can write me on elmarguseinov@yahoo.com.

Comments: 95 Pages.

Download: PDF

Submission history

[v1] 2023-07-11 20:43:09

Unique-IP document downloads: 311 times

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