Computing PI and Szeged indices of multiple phenylenes and cyclic hexagonal-square chain consisting of mutually isomorphic hexagonal chains

Abstract

PI and Szeged indices are two of the most important topological indices defined in chemistry. In this study, the PI and Szeged indices of linear [n]-phenylenes and a cyclic hexagonal-square chain consisting of n mutually isomorphic hexagonal chains were computed. The PI and Szeged indices of a multiple phenylene, which is the 2-dimensional case of a phenylenic nanotube and nanotorus, were determined.

Heliphenes and Related Structures

“…At this point one should make a distinction between regular or semiregular tilings where all vertices are equivalent, which are discussed in the present paper, and non-regular tilings, where there are differences among vertices: one such "biphenylene sheet" [42,43] contains 4-, 6-, and 8-membered rings, and has a third of the vertices common to one 6-membered and two 8-membered rings, with the remaining vertices common to one 4-membered, one 6-membered, and one 8-membered ring (therefore in order to make this net planar, these polygons cannot have normal bond angles). From this "biphenylene sheet" one cannot obtain bent or kinked [n]phenylenes, because it contains only linear [n]phenylene fragments.…”

Degree-based indices computation for special chemical molecular structures using edge dividing method

“…In this section, we consider the degree based indices of benzenoid systems and phenylenes (the structure can refer to Rada et al, [53], Cyvin and Brunvoll [54], Pavlovic and Gutman [55], Yousefi-Azari et al, [56], and Xiao et al, [57]). Note that coves, fjords, fissures, bays and lagoons are basic structural characteristics of the perimeter of the benzenoid systems which can refer to Figure 10.…”

Computing eccentric connectivity index of nanostar dendrimers

“…Each successive repeat unit along all branches forms the next generation, 1 st generation and 2 nd generation and so on until the terminating generation. The topological study of these macromolecules is the aim of following articles, see (Khoramdel et al, 2008;Ashrafi et al, 2008;Karbasioun et al, 2009;Yousefi-Azari et al, 2008) for details. Now, we introduce some notation and terminology.…”