PI Polynomial of V-Phenylenic Nanotubes and Nanotori

Abstract

Abstract:The PI polynomial of a molecular graph is defined to be the sum X |E(G)|−N(e) + |V(G)|(|V(G)|+1)/2 − |E(G)| over all edges of G, where N(e) is the number of edges parallel to e. In this paper, the PI polynomial of the phenylenic nanotubes and nanotori are computed. Several open questions are also included.

New results on eccentric connectivity indices of V-Phenylenic nanotube

“…In this section, we computed the Ediz eccentric connectivity and augmented eccentric connectivity indices of V-Phenylenic nanotube VPHX[p;q]. For further details and more study about the V-Phenylenic nanotube VPHX[p;q] see [31][32][33][34][35][36][37][38][39]. Rao and Lakshmi calculated some eccentric connectivity index of V-Phenylenic nanotube [52].…”

Computing Sanskruti Index of v-Phenylenic Nanotubes and Nanotori

“…The general representation of these nano structures are shown in Figure 1 and Figure 2. For more information and background materials, refer to paper series [12]- [33] again. Now we have following theorems, immediately.…”

“…where S u is the summation of degrees of all neighbors of vertex u in G. In Refs [12]- [27] some topological indices of V −phenylenic nanotube and V −phenylenic nanotori are computed. In this paper, we continue this work to compute the Sanskruti index of molecular graphs related to V −phenylenic nanotube and nanotori.…”

Untitled

“…The novel Phenylenic and Naphthylenic lattices proposed can be constructed from a square net embedded on the toroidal surface. For a review, historical details and further bibliography see the references [36][37][38][39][40][41][42][43][44] . Before presenting the main results, let us introduce following definition.…”