Structural Analysis of Octagonal Nanotubes via Double Edge-Resolving Partitions

In materials science, the open nanotube derived from an octagonal grid is one of the most important and extensively researched compounds. Finding strategies for representing a variety of chemical compounds so that different compounds can have different representations is necessary for the investigation of chemical structures. In this work, the double edge-based resolving partition is discussed and the exchange property applied. Let Q1 and Q2 be two edge-resolving partition sets and Q1≠Q2, such that Q1∩Q2≠0. This shows that this structure has exchange property for edge partition. The exchange property in edge partitions is a novel work. It is introduced in this paper. The application of this work is to transform projects or objects to better places. The resolvability of these compounds is studied to gain an understanding of the chemical composition of the compounds. We perform this by using the terms vertex and edge-based distance and edge-resolving sets of graphs.