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 which frequently appear in chemical, medical and material engineering, as well as the nanotubes: $TUC_4 C_8(S)$, $TUC_4 C_8(R)$, Zig-Zag $TUHC_{6}$, $TUC_4$, Armchair $TUVC_{6}$, then dendrimers $T_{k,d}$ and the circumcoronene series of benzenoid $H_k$. In addition, the irregularities of Mycielski's constructions of cycle and path graphs are analyzed.