Abstract. We give three proofs, two intrinsic and one extrinsic, that every Dickson-Ganley unital U(σ), parametrized by a field automorphism σ, is non-classical if σ is not the identity, extending a result of Ganley's (Math Z 128:34-42, 1972); we prove that U(σ1) is isomorphic to U(σ2) if and only if σ1 = σ2 or σ1 = σ −1 2 ; and we determine the (design) automorphism group of U(σ) as the collineation subgroup of the ambient Dickson semifield plane stabilizing the unital. This contains as a special case the corresponding result of O'Nan's (J Algebra 20:495-511, 1965) on the classical unital.
Mathematics Subject Classification (2000). 51A35, 05B05, 17A35, 51A10, 51A45.
This paper is devoted to estimates of the spanning tree congestion for some planar graphs. We present three main results: (1) We almost determined (up to ±1) the maximal possible spanning tree congestion for planar graphs. (2) The value of congestion indicator introduced by Ostrovskii [Discrete Math. 310, 1204-1209] can be very far from the value of the spanning tree congestion. (3) We find some more examples in which the congestion indicator can be used to find the exact value of the spanning tree congestion.
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