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Summary
Let L-n be the linear phenylene. Then let be the molecular graph obtained from L-n by connecting each pair of non-adjacent vertices on each 4-cycle of L-n by an edge. In this paper, according to the decomposition theorem of Laplacian polynomial, we study the Laplacian spectra of L-n and respectively. By applying the relationship between the roots and coefficients of the characteristic polynomial of L-n (resp. ), explicit closed formulae of Kirchhoff index and the number of spanning trees of L-n and are, respectively, derived in terms of the corresponding Laplacian spectrum. Furthermore, it is surprising to find that the Kirchhoff index of L-n is approximately to one half of its Wiener index, whereas the Kirchhoff index of is approximately to of its Wiener index.
