Abstract
Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1≤k-a1-c2/c2-1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph or a Hamming graph.
Original language | English |
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Pages (from-to) | 227-235 |
Number of pages | 9 |
Journal | European Journal of Combinatorics |
Volume | 26 |
Issue number | 2 |
DOIs | |
State | Published - 1 Feb 2005 |
Keywords
- Distance-regular graph
- Dual polar graph
- Hamming graph
- Near polygon
- Q-polynomial