摘要：An octagon quadrangle is the graph consisting of an 8-cycle ( x 1, x 2,..., x 8) with two additional chords: the edges { x 1, x 4} and { x 5, x 8}. 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 λ K ν defined on X . An octagon quadrangle system Σ=( X , H ) of order ν and index λ is said to be upper C 4-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.
