On a Conjecture of Bannai and Ito: There are Finitely Many Distance-regular Graphs with Degree 5, 6 or 7 |
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| Authors: | J. H. Koolen |
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| Affiliation: | a Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, San 31, Hyoja-dong, Nangu, Pohang, 790-784 Koreaf1;b Linnaeus Center for Bioinformatics, Uppsala University, Box 598, 75124 Uppsala, Swedenf2 |
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| Abstract: | Bannai and Ito conjectured in a 1987 paper that there are finitely many distance-regular graphs with fixed degree that is greater than two. In a series of papers they showed that their conjecture held for distance-regular graphs with degrees 3 or 4. In this paper we prove that the Bannai–Ito conjecture holds for degrees 5–7. |
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