scholarly journals The Laplacian spectral radius for unicyclic graphs with given independence number

2010 ◽  
Vol 433 (5) ◽  
pp. 934-944 ◽  
Author(s):  
Lihua Feng ◽  
Guihai Yu ◽  
Aleksandar Ilić
Keyword(s):  
Spectral Radius ◽  
Independence Number ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs

scholarly journals The Laplacian Spectral Radius of a Class of Unicyclic Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Haixia Zhang
Keyword(s):  
Spectral Radius ◽  
Cycle Length ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs

LetC(n,k)be the set of all unicyclic graphs withnvertices and cycle lengthk. For anyU∈C(n,k),Uconsists of the (unique) cycle (sayCk) of lengthkand a certain number of trees attached to the vertices ofCkhaving (in total)n-kedges. If there are at most two trees attached to the vertices ofCk, wherekis even, we identify in the class of unicyclic graphs those graphs whose Laplacian spectral radii are minimal.

scholarly journals The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Haixia Zhang
Keyword(s):  
Spectral Radius ◽  
Laplacian Spectral Radius ◽  
Unicyclic Graphs

We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs withnvertices and diameterd.

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.

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.

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