in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

in this paper pi, szeged and revised szeged indices of an infinite family of ipr fullereneswith exactly 60+12n carbon atoms are computed. a gap program is also presented that isuseful for our calculations.

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

Let G be a connected graph and ξ(G) = Sze(G)−We(G), where We(G) denotes the edge Wiener index and Sze(G) denotes the edge Szeged index of G. In an earlier paper, it is proved that if T is a tree then Sze(T ) = We(T ). In this paper, we continue our work to prove that for every connected graph G, Sze(G) ≥ We(G) with equality if and only if G is a tree. We also classify all graphs with ξ(G) ≤ 5. ...

in theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. among them wiener, szeged and detour indices play significant roles in anticipating chemical phenomena. in the present paper, we study these topological indices with respect to their difference number.