A Note on the Permanental Roots of Bipartite Graphs

Heping Zhang; Shunyi Liu; Wei Li

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 1, page 49-56
  • ISSN: 2083-5892

Abstract

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It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing at least one edge has complex permanental roots.

How to cite

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Heping Zhang, Shunyi Liu, and Wei Li. "A Note on the Permanental Roots of Bipartite Graphs." Discussiones Mathematicae Graph Theory 34.1 (2014): 49-56. <http://eudml.org/doc/267601>.

@article{HepingZhang2014,
abstract = {It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing at least one edge has complex permanental roots.},
author = {Heping Zhang, Shunyi Liu, Wei Li},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {permanent; permanental polynomial; permanental roots},
language = {eng},
number = {1},
pages = {49-56},
title = {A Note on the Permanental Roots of Bipartite Graphs},
url = {http://eudml.org/doc/267601},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Heping Zhang
AU - Shunyi Liu
AU - Wei Li
TI - A Note on the Permanental Roots of Bipartite Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 1
SP - 49
EP - 56
AB - It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing at least one edge has complex permanental roots.
LA - eng
KW - permanent; permanental polynomial; permanental roots
UR - http://eudml.org/doc/267601
ER -

References

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