# 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

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topHeping 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 -

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