On topological indices of nanostar dendrimers and polyomino chains

A numeric quantity which characterizes the whole structure of a graph is called a topological index. The concept of Randić X(H), atom-bond connectivity (ABC) and geometric-arithmetic (GA) topological indices were established in chemical graph theory based on vertex degrees. Later on, other versions of ABC and GA indices were introduced and some of the versions of these indices are recently designed. Dendrimers are recognized as one of the major commercially available nanoscale building blocks, large and complex molecules with well defined chemical structure. The nanostar dendrimer is a part of a new group of macroparticles that appear to be photon funnels just like artificial antennas. A k -polyomino system is a finite 2 -connected plane graph such that each interior face (also called cell) is surrounded by a regular 4k -cycle of length one. In this article, we compute ABC, GA, and Randić indices of two important families of nanostar dendrimers. We also compute fourth version of atom-bond connectivity (ABC₄) index and fifth version of geometric-arithmetic (GA₅) index for graphs of 1 and 2 -polyomino chains of 8 -cycles.