Hexagon quadrangle systems Original Research Article

A hexagon quadrangle system of order image and index image [image] is a pair image, where image is a finite set of n vertices and image is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of image, with vertex set image. A hexagon quadrangle system is said to be a 4-nesting image if the collection of all the 4-cycles contained in the hexagon quadrangles is a image-fold 4-cycle system. It is said to be a 6-nesting image if the collection of 6-cycles contained in the hexagon quadrangles is a image-fold 6-cycle system. It is said to be a image-nesting, briefly a image, if it is both a 4-nesting and a 6-nesting. In this paper we determine completely the spectrum of image for image, image and image, h positive integer.