| Authors: | Belardo, Francesco Li Marzi, Enzo Simić, Slobodan |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Schwenk-like formulas for weighted digraphs | Journal: | AIP Conference Proceedings | Volume: | 1168 | First page: | 1251 | Last page: | 1254 | Conference: | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009; Rethymno, Crete; Greece; 18 September 2009 through 22 September 2009 | Issue Date: | 26-Nov-2009 | ISBN: | 978-0-735-40709-1 | ISSN: | 0094-243X | DOI: | 10.1063/1.3241302 | Abstract: | Recently the study of the spectrum of weighted (di)graphs has attracted the interest of many researchers. Here we express the characteristic polynomial of any (square) matrix A in terms of the determinant of the Coates graph of the matrix B = xI - A. By doing so we are able to generalize the well-known Schwenk's formulas for simple graphs to weighted digraphs. |
Keywords: | Digraphs | Graph characteristic polynomial | Matrix characteristic polynomial | Multigraphs | Weighted graphs | Publisher: | American Institute of Physics |
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