scholarly journals On the signless Laplacian spectral radius of unicyclic graphs with fixed matching number

2015 ◽  
Vol 97 (111) ◽  
pp. 187-197 ◽  
Author(s):  
Jing-Ming Zhang ◽  
Ting-Zhu Huang ◽  
Ji-Ming Guo
Keyword(s):  
Spectral Radius ◽  
Matching Number ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

We determine the graph with the largest signless Laplacian spectral radius among all unicyclic graphs with fixed matching number.

scholarly journals The Signless Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with a Given Girth

10.37236/670 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Ke Li ◽  
Ligong Wang ◽  
Guopeng Zhao
Keyword(s):  
Spectral Radius ◽  
Upper Bound ◽  
Extremal Graph ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Disjoint Cycles ◽  
Signless Laplacian ◽  
Unique Graph ◽  
Bicyclic Graphs

Let $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$ be the set of unicyclic graphs and bicyclic graphs on $n$ vertices with girth $g$, respectively. Let $\mathcal{B}_{1}(n,g)$ be the subclass of $\mathcal{B}(n,g)$ consisting of all bicyclic graphs with two edge-disjoint cycles and $\mathcal{B}_{2}(n,g)=\mathcal{B}(n,g)\backslash\mathcal{B}_{1}(n,g)$. This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in $\mathcal{U}(n,g)$ and $\mathcal{B}(n,g)$, respectively. Furthermore, an upper bound of the signless Laplacian spectral radius and the extremal graph for $\mathcal{B}(n,g)$ are also given.

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