scholarly journals On ordering bicyclic graphs with respect to the Laplacian spectral radius

2011 ◽  
Vol 24 (12) ◽  
pp. 2186-2192 ◽  
Author(s):  
Shuchao Li ◽  
Slobodan K. Simić ◽  
Dejan V. Tošić ◽  
Qin Zhao
Keyword(s):  
Spectral Radius ◽  
Laplacian Spectral Radius ◽  
Bicyclic Graphs

scholarly journals On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jing-Ming Zhang ◽  
Ting-Zhu Huang ◽  
Ji-Ming Guo
Keyword(s):  
Spectral Radius ◽  
Perfect Matchings ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Bicyclic Graphs

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.

scholarly journals The Laplacian spectral radius of bicyclic graphs with a given girth

2010 ◽  
Vol 59 (1) ◽  
pp. 376-381 ◽  
Author(s):  
Mingqing Zhai ◽  
Guanglong Yu ◽  
Jinlong Shu
Keyword(s):  
Spectral Radius ◽  
Laplacian Spectral Radius ◽  
Bicyclic Graphs

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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