Let Γ denote a distance-regular graph with diameter D > 3 and intersection numbers a1 = 0, a2 6= 0, and c2 = 1. We show a connection between the d-bounded property and the nonexistence of… (More)

Let G be a simple connected graph of order n with average 2degree sequence M1 ≥ M2 ≥ · · · ≥ Mn. Let ρ(G) denote the spectral radius of the adjacency matrix of G. We show that for each 1 ≤ l ≤ n and… (More)

We study partially distance-regular graphs and partially walkregular graphs as generalizations of distance-regular graphs and walkregular graphs respectively. We conclude that the partially… (More)

A pooling space is a ranked poset P such that the subposet w+ induced by the elements above w is atomic for each element w of P . Pooling spaces were introduced in [Discrete Mathematics 282:163-169,… (More)

Let Γ denote a distance-regular graph with diameter D and intersection numbers a2 > a1 = 0. We show that for each 1 ≤ d ≤ D−1, if Γ contains no parallelograms of lengths up to d+1 then Γ is d-bounded… (More)