The edge version of Szeged index and vertex version of PI index are defined very recently. They are similar to edge-PI and vertex-Szeged indices, respectively. The different versions of Szeged and PIindices are the most important topological indices defined in Chemistry. In this paper, we compute the edge-Szeged and vertex-PIindices of some important classes of benzenoid systems.

Let Sz(G) and W (G) be the revised Szeged index and the Wiener index of a graph G. Chen, Li, and Liu [European J. Combin. 36 (2014) 237–246] proved that if G is a non-bipartite connected graph of order n ≥ 4, then Sz(G) −W (G) ≥ ( n + 4n− 6 ) /4. Using a matrix method we prove that if G is a non-bipartite graph of order n, size m, and girth g, then Sz(G)−W (G) ≥ n ( m− 3n 4 ) + P (g), where P i...

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.

the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...