Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649698 | Discrete Mathematics | 2008 | 9 Pages |
Abstract
Let ΓΓ be a d -bounded distance-regular graph with diameter d⩾3d⩾3. Suppose that P(x)P(x) is a set of all strongly closed subgraphs containing x and that P(x,i)P(x,i) is a subset of P(x)P(x) consisting of all elements of P(x)P(x) with diameter i . Let L′(x,i)L′(x,i) be the set generated by all joins of the elements in P(x,i)P(x,i). By ordering L′(x,i)L′(x,i) by inclusion or reverse inclusion, L′(x,i)L′(x,i) is denoted by LO′(x,i) or LR′(x,i). We prove that LO′(x,i) and LR′(x,i) are both finite atomic lattices, and give the conditions for them both being geometric lattices. We also give the eigenpolynomial of LO′(x,i).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jun Guo, Suogang Gao,