On the Laplacian coefficients of unicyclic graphs with prescribed matching number
| Autor: | Shang-Wang Tan |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Mathematics::Combinatorics Unicyclic graphs Unicyclic graph Graph Theoretical Computer Science Computer Science::Robotics Combinatorics Spanning forest Computer Science::Discrete Mathematics Matching Discrete Mathematics and Combinatorics Laplacian coefficient Laplacian matrix Laplace operator Mathematics Characteristic polynomial |
| Zdroj: | Discrete Mathematics. 311(8-9):582-594 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2010.12.022 |
| Popis: | Let @f(G,@l)=@?"k"="0^n(-1)^kc"k(G)@l^n^-^k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. We give some transformations of connected graphs that decrease all Laplacian coefficients c"k(G), we then derive the unicyclic graphs with the minimum Laplacian coefficients in the set of all connected unicyclic graphs with prescribed order and matching number. Furthermore, we determine the unique connected unicyclic graph with the minimal Laplacian coefficients among all connected unicyclic graphs of order n except S"n^', where S"n^' is the unicyclic graph obtained from the n-vertex star S"n by joining two of its pendent vertices with an edge. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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