Octagon Quadrangle Systems nesting 4-kite-designs having equi-indices

• Main Authors: Luigia Berardi, Mario Gionfriddo, Rosaria Rota
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2012-02-01
• Series: Computer Science Journal of Moldova
• Online Access: http://www.math.md/files/csjm/v19-n3/v19-n3-(pp320-332).pdf

An octagon quadrangle is the graph consisting of an 8-cycle (x1,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X,Β), where X is a finite set of v vertices and Β is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKv defined on X. A 4-kite is the graph having five vertices x1, x2, x3, x4, y and consisting of an 4-cycle (x1, x2,..., x4) and an additional edge {x1,y}. A 4-kite design of order n and index μ is a pair K=(Y, H), where Y is a finite set of n vertices and H is a collection of edge disjoint 4-kite which partition the edge set of μKn defined on Y. An Octagon Kite System [OKS] of order v and indices (λ, μ) is an OQS(v) of index λ in which it is possible to divide every block in two 4-kites so that an 4-kite design of order v and index μ is defined. In this paper we determine the spectrum for OKS(v) nesting 4-kite-designs of equi-indices (2,3).