Counting polynomials are important graph invariants whose coefficients and exponents are related to different properties of chemical graphs. Three closely related polynomials, i.e., Omega, Sadhana, and PI polynomials, dependent upon the equidistant edges and nonequidistant edges of graphs, are studied for quasi-hexagonal benzenoid chains. Analytical closed expressions for these polynomials are derived. Moreover, relation between Padmakar–Ivan (PI) index of quasi-hexagonal chain and that of corresponding linear chain is also established.

中文翻译：

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拟六角形Benzenoid链的Omega，Sadhana和PI多项式。

多项式计数是重要的图不变式，其系数和指数与化学图的不同性质有关。对于拟六边形的Benzenoid链，研究了三个紧密相关的多项式，即Omega，Sadhana和PI多项式，具体取决于图的等距边和非等距边。推导了这些多项式的解析式。此外，还建立了准六边形链的Padmakar–Ivan（PI）指数与相应线性链的指数之间的关系。