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IMCS/Publications/CSJM/Issues/CSJM v.18, n.3 (54), 2010/

Perfect Octagon Quadrangle Systems with an upper C4-system and a large spectrum

Authors: Luigia Berardi, Mario Gionfriddo, Rosaria Rota

Abstract

An octagon quadrangle is the graph consisting of an 8-cycle (x1, x2,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order ν and index λ [OQS] is a pair (X,H), where X is a finite set of ν vertices and H is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKν defined on X. An octagon quadrangle system Σ=(X,H) of order ν and index λ is said to be upper C4-perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν; it is said to be upper strongly perfect, if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν and also the collection of all of the outside 8-cycles contained in the octagon quadrangles form a ρ-fold 8-cycle system of order ν. In this paper, the authors determine the spectrum for these systems, in the case that it is the largest possible.

Luigia Berardi,
Dipartimento di Ingegneria Elettrica e dell'Informazione,
Universitá di L'Aquila
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Mario Gionfriddo,
Dipartimento di Matematica e Informatica,
Universitá di Catania
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Rosaria Rota,
Dipartimento di Matematica, Universitá di RomaTre
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