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. This article will provide 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_v is employed to construct the starter of cyclic ((v-1)/2)-star decomposition of 2K_v. These starters were then decomposed into triples and classified as a starter of a cyclic Butterfly triple system. The obtained starter set generated a triple system of order A special reference for case 𝑣𝑣 ≡ 9 (mod 12) was presented to demonstrate the development of the Butterfly triple system.