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. © 2009 American Institute of Physics.
Schwenk-Like Formulas for Weighted Digraphs
BELARDO, FRANCESCO;LI MARZI, Enzo;
2009-01-01
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. © 2009 American Institute of Physics.File in questo prodotto:
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