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Zbl 1185.05101
Walikar, H.B.; Ramane, H.S.
Laplacian polynomial and number of spanning trees in terms of characteristic polynomial of induced subgraphs. (English)
[J] AKCE Int. J. Graphs Comb. 5, No. 1, 47-55 (2008). ISSN 0972-8600

Summary: 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.

MSC 2000:: *05C50 Graphs and matrices
05C05 Trees

Keywords: Laplacian polynomial; characteristic polynomial; number of spanning trees

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