On the irregularity of some molecular structures

Abstract

Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties such as melting and boiling points, toxicity, and resistance. Here, we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees, and the Collatz–Sinogowitz index. Through the means of graph structural analysis and derivation, we study the above-mentioned irregularity measures of several chemical molecular graphs that frequently appear in chemical, medical, and material engineering, as well as the nanotubes: TUC4C8(S), TUC4C8(R), zigzag TUHC6, TUC4, Armchair TUVC6, then dendrimers Tk,d, and the circumcoronene series of benzenoid Hk. In addition, the irregularities of Mycielski’s constructions of cycle and path graphs are analyzed.