Decompositions of Hypercube Graphs into Diametral Paths and Cycle Decompositions

Abstract

One of the most well-known and well-studied issues in graph theory is graph decomposition. Graph decomposition has been studied in great detail by extensive research. There are two main types of decomposition problems such as edge decompositions and vertex decompositions. It entails meeting certain requirements in order to divide an input graph into smaller segments (subgraphs). In this paper, an investigation into decomposition in hypercube graphs using diametral routes is studied. Additionally, we study the finding of the diametral path decomposition number, index, and hypercube graph's cycle decomposition.