Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648527 | Discrete Mathematics | 2011 | 13 Pages |
Abstract
Let ϕ(G,λ)=∑k=0n(−1)kck(G)λn−k be the characteristic polynomial of the Laplacian matrix of a graph GG of order nn. We give some transformations of connected graphs that decrease all Laplacian coefficients ck(G)ck(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 nn except Sn′, where Sn′ is the unicyclic graph obtained from the nn-vertex star SnSn by joining two of its pendent vertices with an edge.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Shang-wang Tan,