On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number
Let φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k$\phi (L(G)) = \det (xI - L(G)) = \sum\nolimits_{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢n,n+2(i) (the set of...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2017-08-01
|
| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1937 |
| _version_ | 1797757767373553664 |
|---|---|
| author | Luo Jing Zhu Zhongxun Wan Runze |
| author_facet | Luo Jing Zhu Zhongxun Wan Runze |
| author_sort | Luo Jing |
| collection | DOAJ |
| description | Let
φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k$\phi (L(G)) = \det (xI - L(G)) = \sum\nolimits_{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $
be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in 𝒢n,n+2(i). |
| first_indexed | 2024-03-12T18:20:13Z |
| format | Article |
| id | doaj.art-7c98a70f4cbd4b1eac6f012632163527 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:20:13Z |
| publishDate | 2017-08-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-7c98a70f4cbd4b1eac6f0126321635272023-08-02T08:59:08ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922017-08-0137350552210.7151/dmgt.1937dmgt.1937On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching NumberLuo Jing0Zhu Zhongxun1Wan Runze2Department of Mathematics and Statistics, South Central University for Nationalities, Wuhan430074, P.R. ChinaDepartment of Mathematics and Statistics, South Central University for Nationalities, Wuhan430074, P.R. ChinaCollege of Computer, Hubei University of Education, Wuhan430205, P.R. ChinaLet φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k$\phi (L(G)) = \det (xI - L(G)) = \sum\nolimits_{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in 𝒢n,n+2(i).https://doi.org/10.7151/dmgt.1937laplacian characteristic polynomiallaplacian-like energytricyclic graph05c1205c50 |
| spellingShingle | Luo Jing Zhu Zhongxun Wan Runze On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number Discussiones Mathematicae Graph Theory laplacian characteristic polynomial laplacian-like energy tricyclic graph 05c12 05c50 |
| title | On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number |
| title_full | On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number |
| title_fullStr | On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number |
| title_full_unstemmed | On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number |
| title_short | On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number |
| title_sort | on the laplacian coefficients of tricyclic graphs with prescribed matching number |
| topic | laplacian characteristic polynomial laplacian-like energy tricyclic graph 05c12 05c50 |
| url | https://doi.org/10.7151/dmgt.1937 |
| work_keys_str_mv | AT luojing onthelaplaciancoefficientsoftricyclicgraphswithprescribedmatchingnumber AT zhuzhongxun onthelaplaciancoefficientsoftricyclicgraphswithprescribedmatchingnumber AT wanrunze onthelaplaciancoefficientsoftricyclicgraphswithprescribedmatchingnumber |