Edge functions T1 and T2, which describe the polarization-dependent edge contribution to forward scattering by spheres, are derived from the exact Mie solution. All the relative refractive indices and the 64 < x < 2048 size parameter range are considered. The edge functions significantly improve the approximation methods that can be used to calculate forward-scattering patterns. For m close to ...

Chemical Graph Theory is a branch of Mathematical Chemistry whose focus interest to finding topological indices chemical graphs which correlate well with properties the molecules. In this study, we define edge version Sombor index, modified index and, Nirmala graph and compute exact formulas for certain families nanotubes nanotori.

For a given connected graph G of order n, a routing R is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passing through any vertex (resp. edge) in the graph. In this paper, the authors determine the vertex and the edge forwarding indices of a folded n-cube as (n− 1)2n−1...

This study used hyperspectral reflectance data to evaluate the crop physiological parameters of sweet maize. Principal component analysis (PCA) was applied identify wavelengths that primarily contributed each selected PC. Correlation and multiple linear regression, with a stepwise algorithm, were select best-performing vegetation indices (VIs) for monitoring yield response maize grown under dif...

We extend our previous work on complexity indices for the travelling salesman problem (TSP) using graph spectral techniques of data mining. A complexity index is an invariant of an instance I by which we can predict the execution time of an exact algorithm for TSP for I. We consider the symmetric travelling salesman problem with instances I represented by complete weighted graphs G. Intuitively...

In this paper we examine the interaction of stock markets of different countries by constructing networks that connect 32 selected stock market indices from different countries. In the network being constructed, the nodes are the stock market indices and the edges are connections between the indices. Each edge has an edge weight equal to the cross-correlation between the pair of connecting indi...

A routing R of a given connected graph G of order n is a collection of n(n−1) simple paths connecting every ordered pair of vertices of G. The vertexforwarding index ξ(G,R) of G with respect to R is defined as the maximum number of paths in R passing through any vertex of G. The vertex-forwarding index ξ(G) of G is defined as the minimum ξ(G,R) over all routing R’s of G. Similarly, the edge-for...