  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.
