Kirchhoff Indices and Numbers of Spanning Trees of Molecular Graphs Derived from Linear Crossed Polyomino Chain

Polyomino systems are widely studied in organic chemistry, especially in polycyclic aromatic compounds. Let Q(n) 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 Q(n). 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 Q(n) are obtained. Moreover, their Kirchhoff indices are shown to be almost one quarter of their Wiener indices.