the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....

in this paper, at first we mention to some results related to pi and vertex co-pi indices and then we introduce the edge versions of co-pi indices. then, we obtain some properties about these new indices.

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

The edge Szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph G, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. In this paper, the edge Szeged index of one-pentagonal carbon nanocone CNC5[n] is computed for the first ...

structural codes vis-a-vis structural counts, like polynomials of a molecular graph, areimportant in computing graph-theoretical descriptors which are commonly known astopological indices. these indices are most important for characterizing carbon nanotubes(cnts). in this paper we have computed sadhana index (sd) for phenylenes and theirhexagonal squeezes using structural codes (counts). sadhan...

Abstract Deep learning methods applied to chemistry can be used accelerate the discovery of new molecules. This work introduces GraphINVENT, a platform developed for graph-based molecular design using graph neural networks (GNNs). GraphINVENT uses tiered deep network architecture probabilistically generate molecules single bond at time. All models implemented in quickly learn build resembling t...

The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the w...

It seems that the general applicability of the quantum theory of atoms in molecules (QTAIM) oncharacterizing the bonded interactions is still questionable even afier 30 years since its formulation. Fordemonstrating the generality of bonding schemes in QTA IM, ea( isomers were chosen as the modelsystems and the results from molecular charge density analysis and vibrational normal modes werecompa...