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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2014-02-01
|
| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1704 |
| _version_ | 1797718054183895040 |
|---|---|
| author | Zhang Heping Liu Shunyi Li Wei |
| author_facet | Zhang Heping Liu Shunyi Li Wei |
| author_sort | Zhang Heping |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-12T08:45:24Z |
| format | Article |
| id | doaj.art-faf0019ceedc484480424a2a1dd7630a |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T08:45:24Z |
| publishDate | 2014-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-faf0019ceedc484480424a2a1dd7630a2023-09-02T16:29:32ZengUniversity of Zielona GóraDiscussiones 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 |
| 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 |
| title | 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_short | A Note on the Permanental Roots of Bipartite Graphs |
| title_sort | note on the permanental roots of bipartite graphs |
| 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 |