Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416331 | Linear Algebra and its Applications | 2015 | 24 Pages |
Abstract
Let Î be a Q-polynomial distance-regular graph with diameter at least 3. Terwilliger (1993) implicitly showed that there exists a polynomial, say T(λ)âR[λ], of degree 4 depending only on the intersection numbers of Î and its Q-polynomial ordering and such that T(η)â¥0 holds for any non-principal eigenvalue η of the local graph Î(x) for any vertex xâV(Î).We call T(λ) the Terwilliger polynomial of Î. In this paper, we give an explicit formula for T(λ) in terms of the intersection numbers of Î and the dual eigenvalues of Î with respect to the first primitive idempotent in its Q-polynomial ordering. We then apply this polynomial to show that all pseudo-partition graphs with diameter at least 3 are known.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexander L. Gavrilyuk, Jack H. Koolen,