Perfect octagon quadrangle systems—II

An octagon quadrangle   [OQOQ] is the graph consisting of an 8-cycle (x1,x2,…,x8)(x1,x2,…,x8) with the two additional edges {x1,x4}{x1,x4} and {x5,x8}{x5,x8}. An octagon quadrangle system   of order vv and index λλ [OQSOQS or OQSλ(v)OQSλ(v)] is a pair (X,H)(X,H), where XX is a finite set of vv vertices and HH is a collection of edge disjoint OQsOQs (blocks  ) which partition the edge set of λKvλKv defined on XX. In this paper (i) C4C4-perfect   OQSλ(v)OQSλ(v), (ii) C8C8-perfect   OQSλ(v)OQSλ(v) and (iii) strongly perfect   OQSλ(v)OQSλ(v) are studied for λ=10λ=10, that is the smallest index for which the spectrum of the admissible values of vv is the largest possible. This paper is the continuation of Berardi et al. (2010) [1], where the spectrum is determined for λ=5λ=5, that is the index for which the spectrum of the admissible values of vv is the minimum possible.