Butterfly Triple System Algorithm Based on Graph Theory

Abstract

In combinatorial design theory, clustering elements into a set of three elements is the heart of classifying data, which has recently received considerable attention in the fields of network algorithms, cryptography, design and analysis of algorithms, statistics, and Information theory. This article provides insight into formulating algorithm for a new type of triple system, called a Butterfly triple system. Basically, in this algorithm development, a starter of cyclic near-resolvable ((v-1)/2)-cycle system of the 2-fold complete graph 2K_vis employed to construct the starter of cyclic ((v-1)/2)-star decomposition of 2K_v. These starters are then decomposed into triples and classified as a starter of cyclic Butterfly triple. The obtained starter set generates a triple system of order v. A special reference for case ν ≡ 9 (mod 12) is presented to demonstrate the development of the Butterfly triple system.