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Let F q be a finite field, where q = p e for some odd prime p and integer e ≥ 1. proved in [6] that if p ≥ 5 and e = 2 a 3 b for integers a, b ≥ 0, then all monomial graphs G q (f, g) of girth at least eight are isomorphic to G q (xy, xy 2), an induced subgraph of the point-line incidence graph of a classical generalized quadrangle of order q. In this… (More)

Let F be a field. For a polynomial f ∈ F[x, y], we define a bipartite graph Γ F (f) with vertex partition

In this paper, we prove a closed form for a sequence motivated by the search for new generalized quadrangles of odd order. We present two proofs: a direct proof to explain the closed form's derivation and a shorter inductive argument. The sequence in question is derived from congruences that arise from applying the Hermite-Dickson criterion to a permutation… (More)

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