Hexagon kite systems

Octagon kite systems

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Abstract The spectrum of octagon kite system (OKS) which is nesting strongly balanced 4-kite-designs is determined.

Hexagon biquadrangle systems

Hexagon quadrangle systems

A hexagon quadrangle system of order n and index [HQS (n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of Kn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4) − HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a /2-fo...

Kite systems of order 8; embedding of kite systems into bowtie systems

This article consist of two parts. In the first part, we enumerate the kite systems of order 8; in the second part, we consider embedding kite systems into bowtie systems.

Embedding path designs into kite systems

Let D be the triangle with an attached edge (i. e. D is the “kite”, a graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). Bermond and Schönheim [6] proved that a kite-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial kite-design of order n ≥ 8, and let V ⊂ W with |V | = v < n. A path design (V,P) of order v and block siz...