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- W2950365300 abstract "Let $G$ denote a bipartite distance-regular graph with vertex set $X$ and diameter $D ge 3$. Fix $x in X$ and let $L$ (resp. $R$) denote the corresponding lowering (resp. raising) matrix. We show that each $Q$-polynomial structure for $G$ yields a certain linear dependency among $RL^2$, $LRL$, $L^2R$, $L$. Define a partial order $le$ on $X$ as follows. For $y,z in X$ let $y le z$ whenever $partial(x,y)+partial(y,z)=partial(x,z)$, where $partial$ denotes path-length distance. We determine whether the above linear dependency gives this poset a uniform or strongly uniform structure. We show that except for one special case a uniform structure is attained, and except for three special cases a strongly uniform structure is attained." @default.
- W2950365300 created "2019-06-27" @default.
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- W2950365300 date "2011-08-11" @default.
- W2950365300 modified "2023-10-11" @default.
- W2950365300 title "Bipartite Q-polynomial distance-regular graphs and uniform posets" @default.
- W2950365300 hasPublicationYear "2011" @default.
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