On the Irregularity of Some Molecular Structures

2016/08/18 by Hosam Abdo, Abdo, Hosam, Darko Dimitrov +3
Chemistry · Computer Science · Mathematics · #Computational Drug Discovery Methods #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph theory and applications #History and advancements in chemistry

paper · pdf · doi:10.48550/arxiv.1608.05235

openalex publication_date 2016/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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: TUC₄ C₈(S), TUC₄ C₈(R), Zig-Zag TUHC₆, TUC₄, Armchair TUVC₆, 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.

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