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December 2007 Singular Distance Powers of Circuits
Torsten SANDER
Tokyo J. Math. 30(2): 489-496 (December 2007). DOI: 10.3836/tjm/1202136691

Abstract

In this work a precise condition for the singularity of a circuit distance power $C_n^{(d)}$ is derived. Namely, either $n$ and $d$ are not relatively prime or the order of 2 in $d+1$ is strictly smaller than in $n$. It is also shown that the simple eigenvalues of circuit distance powers are contained in $\{-2,0,2d\}$, generalizing a well-known result for circuits. Further, the nullity of $C_n^{(d)}$ is calculated.

Citation

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Torsten SANDER. "Singular Distance Powers of Circuits." Tokyo J. Math. 30 (2) 489 - 496, December 2007. https://doi.org/10.3836/tjm/1202136691

Information

Published: December 2007
First available in Project Euclid: 4 February 2008

zbMATH: 1172.05040
MathSciNet: MR2376524
Digital Object Identifier: 10.3836/tjm/1202136691

Subjects:
Primary: 05C50
Secondary: 15A18‎

Rights: Copyright © 2007 Publication Committee for the Tokyo Journal of Mathematics

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Vol.30 • No. 2 • December 2007
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