Enumeration of spanning trees in a chain of diphenylene graphs. (2nd January 2022)

• Record Type: Journal Article
• Authors: Modabish, Abdulhafid; Husin, Mohamad Nazri; Alameri, Abdu Qaid; Ahmed, Hanan; Alaeiyan, Mehdi; Farahani, Mohammed Reza; Cancan, Murat
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 25:Number 1(2022)
• Page Start: 241
• Page End: 251
• Publication Date: 2022-01-02
• Subjects: 05C85 -- 05C30; Spanning trees -- Laplacian matrix -- Diphenylene -- Chain of diphenylene; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2022.2038931
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: Cheminformatics is a modern field of chemistry information science and mathematics that is very much helpful in keeping the data and getting information about chemicals. A new two-dimensional carbon known as diphenylene was identified and synthesized. It is considered one of the materials that have many applications in most fields such as catalysis. The number of spanning trees of a graph G, also known as the complexity of a graph G, denoted by τ ( G ), is an important, well-studied quantity in graph theory, and appears in a number of applications. In this paper, we introduce a new chemical compound that is a chain of diphenylene where any two diphenylene intersect by one edge. We derive two formulas for the number of spanning trees in a chain of diphenylene planar graphs that have connected intersection of one edge but where the diphenylenes have same sizes.