Perfect octagon quadrangle systems—II

An octagon quadrangle [ O Q ] is the graph consisting of an 8-cycle ( x 1 , x 2 , … , x 8 ) with the two additional edges { x 1 , x 4 } and { x 5 , x 8 } . An octagon quadrangle system of order v and index λ [ O Q S or O Q S λ ( v ) ] is a pair ( X , H ) , where X is a finite set of v vertices and H is a collection of edge disjoint O Q s (blocks) which partition the edge set of λ K v defined on X . In this paper (i) C 4 -perfect  O Q S λ ( v ) , (ii) C 8 -perfect  O Q S λ ( v ) and (iii) strongly perfect  O Q S λ ( v ) are studied for λ = 10 , that is the smallest index for which the spectrum of the admissible values of v is the largest possible. This paper is the continuation of Berardi et al. (2010) [1], where the spectrum is determined for λ = 5 , that is the index for which the spectrum of the admissible values of v is the minimum possible.