A Note on the Permanental Roots of Bipartite Graphs

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...

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Main Authors:	Zhang Heping, Liu Shunyi, Li Wei
Format:	Article
Language:	English
Published:	Sciendo 2014-02-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	permanent permanental polynomial permanental roots
Online Access:	https://doi.org/10.7151/dmgt.1704

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spelling	doaj-faf0019ceedc484480424a2a1dd7630a2021-09-05T17:20:20ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922014-02-01341495610.7151/dmgt.1704dmgt.1704A Note on the Permanental Roots of Bipartite GraphsZhang Heping0Liu Shunyi1Li Wei2School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, P.R. ChinaSchool of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, P.R. ChinaSchool of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, P.R. ChinaIt 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.https://doi.org/10.7151/dmgt.1704permanentpermanental polynomialpermanental roots
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zhang Heping Liu Shunyi Li Wei
spellingShingle	Zhang Heping Liu Shunyi Li Wei A Note on the Permanental Roots of Bipartite Graphs Discussiones Mathematicae Graph Theory permanent permanental polynomial permanental roots
author_facet	Zhang Heping Liu Shunyi Li Wei
author_sort	Zhang Heping
title	A Note on the Permanental Roots of Bipartite Graphs
title_short	A Note on the Permanental Roots of Bipartite Graphs
title_full	A Note on the Permanental Roots of Bipartite Graphs
title_fullStr	A Note on the Permanental Roots of Bipartite Graphs
title_full_unstemmed	A Note on the Permanental Roots of Bipartite Graphs
title_sort	note on the permanental roots of bipartite graphs
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2014-02-01
description	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.
topic	permanent permanental polynomial permanental roots
url	https://doi.org/10.7151/dmgt.1704
work_keys_str_mv	AT zhangheping anoteonthepermanentalrootsofbipartitegraphs AT liushunyi anoteonthepermanentalrootsofbipartitegraphs AT liwei anoteonthepermanentalrootsofbipartitegraphs AT zhangheping noteonthepermanentalrootsofbipartitegraphs AT liushunyi noteonthepermanentalrootsofbipartitegraphs AT liwei noteonthepermanentalrootsofbipartitegraphs
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A Note on the Permanental Roots of Bipartite Graphs

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