Lower bounds for the number of inlets of hexagonal systems. Issue 19 (11th July 2020)

• Record Type: Journal Article
• Authors: Cruz, Roberto; Duque, Frank; Rada, Juan
• Is Part Of: International journal of quantum chemistry. Volume 120:Issue 19(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-07-11
• Subjects: hexagonal systems -- number of inlets -- vertex degree based topological indices; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.26358
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: The number of inlets of a hexagonal system H is denoted by r ( H ) and defined as the sum of the fissures, bays, coves, and fjords of H . It is well known that the parameter r plays an important role in the theory of molecular descriptors. Let Λ n and Γ m denote the set of hexagonal systems with n vertices and m edges, respectively. In this paper we find sharp lower bounds for the number of inlets on Λ n and Γ m . As a consequence, we determine extremal values of the Randić, harmonic, and geometric‐arithmetic indices over Λ n and Γ m . Graphical Abstract: The number of inlets of a hexagonal system plays an important role in the theory of molecular descriptors. One important problem in chemical graph theory is to determine extremal values of a vertex‐degree‐based topological index over the sets Λ n and Γ m, which are conformed by hexagonal systems with n vertices and m edges, respectively. To do this, it is important to know the extreme values of the number of inlets in Λ n and Γ m . The construction of hexagonal systems with minimal number of inlets in Λ n, for n = 24 s 2 + 18 s + 6 with s = 1, 2, …, is depicted in this figure.