An octagon quadrangle [OQ] is the graph consisting of an 8-cycle (x1, x2, . . . , x8) with the two additional edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS or OQSλ(v)] is a pair (X, H), where X is a finite set of v vertices and H is a collection of edge disjoint OQs (blocks) which partition the edge set of λKv defined on X. In this paper (i) C4-perfect OQSλ(v), (ii) C8-perfect OQSλ(v) and (iii) strongly perfect OQSλ(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.
Perfect Octagon Quadrangle Systems - II
GIONFRIDDO, Mario;
2012-01-01
Abstract
An octagon quadrangle [OQ] is the graph consisting of an 8-cycle (x1, x2, . . . , x8) with the two additional edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS or OQSλ(v)] is a pair (X, H), where X is a finite set of v vertices and H is a collection of edge disjoint OQs (blocks) which partition the edge set of λKv defined on X. In this paper (i) C4-perfect OQSλ(v), (ii) C8-perfect OQSλ(v) and (iii) strongly perfect OQSλ(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
