Abstract.
Let Γ denote a bipartite distance-regular graph with diameter D≥12. We show Γ is Q-polynomial if and only if one of the following (i)–(iv) holds: (i) Γ is the ordinary 2D-cycle. (ii) Γ is the Hamming cube H(D,2). (iii) Γ is the antipodal quotient of H(2D,2). (iv) The intersection numbers of Γ satisfy where q is an integer at least 2. We obtain the above result using the Terwilliger algebra of Γ.
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AMS 1991 Subject Classification: Primary 05E30
Final version received: April 10, 2003
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Caughman IV, J. Bipartite Q-Polynomial Distance-Regular Graphs. Graphs and Combinatorics 20, 47–57 (2004). https://doi.org/10.1007/s00373-003-0538-8
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DOI: https://doi.org/10.1007/s00373-003-0538-8