Lattices generated by join of strongly closed subgraphs in d-bounded distance-regular graphs |
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Authors: | Jun Guo |
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Institution: | a Mathematics and Information College, Langfang Teachers’ College, Langfang 065000, PR China b Mathematics and Information College, Hebei Normal University, Shijiazhuang 050016, PR China |
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Abstract: | Let Γ be a d-bounded distance-regular graph with diameter d?3. Suppose that P(x) is a set of all strongly closed subgraphs containing x and that P(x,i) is a subset of P(x) consisting of all elements of P(x) with diameter i. Let L′(x,i) be the set generated by all joins of the elements in P(x,i). By ordering L′(x,i) by inclusion or reverse inclusion, L′(x,i) is denoted by or . We prove that and are both finite atomic lattices, and give the conditions for them both being geometric lattices. We also give the eigenpolynomial of ![View the MathML source View the MathML source](http://ars.els-cdn.com/content/image/1-s2.0-S0012365X07002774-si15.gif) |
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Keywords: | 06C10 |
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