Computing the Szeged Index

We give an explicit algorithm for computing the Szeged index of a graph which runs in O(mn) time, where n is the number of nodes and m is the number of edges

Perfect codes in direct products of cycles—a complete characterization

AbstractLet be a direct product of cycles. It is known that for any r⩾1, and any n⩾2, each connected component of G contains a so-called canonical r-perfect code provided that each ℓi is a multiple of rn+(r+1)n. Here we prove that up to a reasonably defined equivalence, these are the only perfect codes that exist

Improving approximation by switching between two error functions

The key to designing a LED luminaire is the choice of secondary optics. The design process can be improved using analytical models and optimization tools. A modified approximation error (evaluation function) is introduced in the standard analytical model for spatial light distribution. It is shown that the new evaluation function provides better quality and consistency compared to the standard evaluation function, and is a better practical approach to the optimization problem

Computing the Weighted Wiener and Szeged Number on Weighted Cactus Graphs in Linear Time

Cactus is a graph in which every edge lies on at most one cycle. Linear algorithms for computing the weighted Wiener and Szeged numbers on weighted cactus graphs are given. Graphs with weighted vertices and edges correspond to molecular graphs with heteroatoms