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