In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalizedWiener polarity indexWk(G) as the number of unordered pairs of vertices {u, v} of G such that the shortest distance d(u, v) between u and v is k. For k = 3, we get standard Wiener polarity index. ...

TheWiener polarity indexWp(G) of a graphG of order n is the number of unordered pairs of vertices u and v of G such that the distance dG(u, v) between u and v is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and C4 nanotubes and nanotori are computed. AMS Mathematics Subj...

Disruptions of natural texture appearance are known to negatively impact performance in texture discrimination tasks, for example, such that contrast-negated textures, synthetic textures, and textures depicting abstract art are processed less efficiently than natural textures. Presently, we examined how visual ERP responses (the P1 and the N1 in particular) were affected by violations of natura...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index i...