The vertex Padmakar-Ivan (PIv) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork [The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 723-734]. Two efficient formulas for calculating th...

General formulas are obtained for the vertex Padmakar-Ivan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a Wiener-Szeged-like index developed very recently. This topological index is defined as the summation of all sums of nu(e) and nv(e), over all edges of connected graph G.

general formulas are obtained for the vertex padmakar-ivan index (piv) of tetrathiafulvalene(ttf) dendrimer, whereby ttf units we are employed as branching centers. the piv index isa wiener-szeged-like index developed very recently. this topological index is defined as thesummation of all sums of nu(e) and nv(e), over all edges of connected graph g.

Statistical clustering technique is extensively employed in molecular similarity analysis where molecules can be clustered on the basis of Euclidean distances derived from rules measures. Such clusters extremely useful quantitative structure–property relations as any representative within a cluster would have properties similar to other members cluster. Consequently, topological techniques for ...

A large number of medical experiments have confirmed that the features drugs a close correlation with their molecular structure. Drug properties can be obtained by studying structure corresponding drugs. The calculation topological index chemical graph enables scientists to better understanding physical chemistry and biological characteristics In this paper, we focus on Hyaluronic Acid-Curcumin...

The Wiener index of a connected graph G, denoted by W (G), is defined as 12 ∑ u,v∈V (G) dG(u, v). Similarly, the hyper-Wiener index of a connected graph G, denoted by WW (G), is defined as 1 2W (G) + 1 4 ∑ u,v∈V (G) dG(u, v). The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, ...

The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. The PI index of a graph G is the sum of all edges uv of G of the number of edges which are not equidistant from the vertices u and v. In this paper we obtain the second and third extremals of catacondensed hexagonal systems with respect to the PI index.