Abstract
Polyomino systems are widely studied in organic chemistry, especially in polycyclic aromatic compounds. Let Qn be a linear crossed polyomino chain with n complete quadrangles. In this article, we construct a family of molecular graphs obtained by randomly deleting some specified edges of Qn . By using the decomposition theorem of the Laplacian matrix characteristic polynomial, explicit formulas of Kirchhoff indices and numbers of spanning trees of those molecular graphs derived from Qn are obtained. Moreover, their Kirchhoff indices are shown to be almost one quarter of their Wiener indices.
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