Abstract
In this paper, we express the Laplacian polynomial of a graph in terms of the characteristic polynomials of its induced subgraphs. Further the Laplacian polynomial of a regular graph is expressed in terms of derivatives of its characteristic polynomial. In the sequel we obtain the Laplacian polynomial of a complement of a graph in terms of the characteristic polynomial of induced subgraphs of a graph. Using these we obtain the number of spanning trees of a graph.
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