Bipartite Q -Polynomial Distance-Regular Graphs

Bipartite Q -Polynomial Distance-Regular Graphs

Let Gamma denote a bipartite distance-regular graph with diameter Dge12. We show Gamma is Q-polynomial if and only if one of the following (i)-(iv) holds: (i) Gamma is the ordinary 2D-cycle. (ii) Gamma is the Hamming cube H(D,2). (iii) Gamma is the antipodal quotient of H(2D,2). (iv) The intersectio...

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Veröffentlicht in:Graphs and combinatorics 2004-03, Vol.20 (1), p.47-57
1. Verfasser: Caughman IV, John S.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Graphs
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Zusammenfassung:Let Gamma denote a bipartite distance-regular graph with diameter Dge12. We show Gamma is Q-polynomial if and only if one of the following (i)-(iv) holds: (i) Gamma is the ordinary 2D-cycle. (ii) Gamma is the Hamming cube H(D,2). (iii) Gamma is the antipodal quotient of H(2D,2). (iv) The intersection numbers of Gamma satisfy where q is an integer at least 2. We obtain the above result using the Terwilliger algebra of Gamma. [PUBLICATION ABSTRACT]
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-003-0538-8