On the F-index and F-coindex of the line graphs of the subdivision graphs

TL;DR

This paper explores the F-index and F-coindex of line graphs derived from various subdivision graphs, including cycles, stars, and complex lattice structures, expanding understanding of these indices in graph theory.

Contribution

It introduces new calculations of F-index and F-coindex for line graphs of subdivision graphs across multiple graph families and complex lattice structures.

Findings

F-index and F-coindex values for line graphs of cycle, star, tadpole, wheel, and ladder graphs.

F-index of line graphs of subdivision graphs of grid, nanotube, and nanotorus structures.

Extended analysis of F-index for complex lattice graphs like TUC_{4}C_{8}[p, q].

Abstract

The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision graph of square grid graph, 2D-lattice, nanotube and nanotorus of $TUC_{4}C_{8}[p, q]$ are also investigated here.