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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