Analysis of Zigzag and Rhombic Benzenoid Systems via Irregularity Indices

On the total edge irregularity strength of zigzag graphs

An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges with labels 1, 2, . . . , k such that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two end vertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregul...

On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes

Edge-Szeged and vertex-PIindices of Some Benzenoid Systems

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.

Irregularity of Hypergeometric Systems via Slopes along Coordinate Subspaces

We study the irregularity sheaves attached to the A-hypergeometric D-module MA(β) introduced by Gel’fand et al., where A ∈ Z d×n is pointed of full rank and β ∈ C. More precisely, we investigate the slopes of this module along coordinate subspaces. In the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector L on torus...

From Ternary Strings to Wiener Indices of Benzenoid Chains

An explicit, non-recursive formula for the Wiener index of any given benzenoid chain is derived, greatly speeding up calculations and rendering it manually manageable, through a novel envisioning of chains as ternary strings. Previous results are encompassed and two completely new and useful ones are obtained, a formula to determine Wiener indices of benzenoid chains in periodic patterns, and a...