There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter

Details There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter

2010-12-13

arxiv.org/abs/1012.2632v1

Mathematics

Combinatorics

12 pages

Scientific paper

In this paper, we show that for given positive integer C, there are only
finitely many distance-regular graphs with valency k at least three, diameter D
at least six and k2/k<=C. This extends a conjecture of Bannai and Ito.

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