Lower bounds for the number of inlets of hexagonal systems

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 Λn and Γm 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 Λn and Γm. As a consequence, we determine extremal values of the Randić, harmonic, and geometric‐arithmetic indices over Λn and Γm.

Extremal benzenoid systems for two modified versions of the Randić index

“…The extremal benzenoid systems or fluoranthene-type benzenoid systems with respect to several topological indices such as the connectivity index, general connectivity index, second Zagreb index, atom-bond connectivity index, sum-connectivity index, geometric-arithmetic index, augmented Zagreb index, and harmonic index have been determined, and many results concerning this topic can be found in [1,3,5,19,[25][26][27]32,33,36,37,39,41,47] and the references therein.…”

The hyper‐Wiener Index of diamond nanowires

“…Some of the graph indices are calculated for finite segments of some infinite grids and lattices [5,[13][14][15][16] in addition to particular unique molecules. Hexagonal structures are further studied from various points of view in [17,18]. The geometry of infinite periodic discrete structures (or their finite subsets) constructed from points, on the other hand, is the focus of digital geometry.…”