On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs
With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and re...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-06-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2020.00208/full |
| _version_ | 1818135837754261504 |
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| author | Hongyan Lu Zhongxun Zhu |
| author_facet | Hongyan Lu Zhongxun Zhu |
| author_sort | Hongyan Lu |
| collection | DOAJ |
| description | With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and reduce the number of graphs. A sharp lower bound for incidence energy in the tricyclic graphs is given and all the extremal structures are characterized. The most interesting things that we find two different classes tricyclic graphs have the same signless Laplacian characteristic polynomials and one of the extremal graphs beyond all expectations. |
| first_indexed | 2024-12-11T09:30:52Z |
| format | Article |
| id | doaj.art-8b4e48001cc14b7391910c0a241f5f81 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-11T09:30:52Z |
| publishDate | 2020-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-8b4e48001cc14b7391910c0a241f5f812022-12-22T01:13:01ZengFrontiers Media S.A.Frontiers in Physics2296-424X2020-06-01810.3389/fphy.2020.00208544394On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle GraphsHongyan Lu0Zhongxun Zhu1College of Science, Xijing University, Xi'an, ChinaFaculty of Mathematics and Statistics, South Central University for Nationalities, Wuhan, ChinaWith the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and reduce the number of graphs. A sharp lower bound for incidence energy in the tricyclic graphs is given and all the extremal structures are characterized. The most interesting things that we find two different classes tricyclic graphs have the same signless Laplacian characteristic polynomials and one of the extremal graphs beyond all expectations.https://www.frontiersin.org/article/10.3389/fphy.2020.00208/fullincidence energyextremal graphtricyclic graphLaplacian matrixsignless Laplacian coefficients |
| spellingShingle | Hongyan Lu Zhongxun Zhu On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs Frontiers in Physics incidence energy extremal graph tricyclic graph Laplacian matrix signless Laplacian coefficients |
| title | On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs |
| title_full | On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs |
| title_fullStr | On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs |
| title_full_unstemmed | On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs |
| title_short | On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs |
| title_sort | on the boundary of incidence energy and its extremum structure of tricycle graphs |
| topic | incidence energy extremal graph tricyclic graph Laplacian matrix signless Laplacian coefficients |
| url | https://www.frontiersin.org/article/10.3389/fphy.2020.00208/full |
| work_keys_str_mv | AT hongyanlu ontheboundaryofincidenceenergyanditsextremumstructureoftricyclegraphs AT zhongxunzhu ontheboundaryofincidenceenergyanditsextremumstructureoftricyclegraphs |