scholarly journals The smallest eigenvalue distribution of the Jacobi unitary ensembles

2021 ◽  
Author(s):  
Shulin Lyu ◽  
Yang Chen
Keyword(s):  
Eigenvalue Distribution ◽  
Smallest Eigenvalue

scholarly journals On minimum algebraic connectivity of graphs whose complements are bicyclic

2019 ◽  
Vol 17 (1) ◽  
pp. 1490-1502 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Javaid ◽  
Mohsin Raza ◽  
Naeem Saleem
Keyword(s):  
Connected Graph ◽  
Diffusion Processes ◽  
Laplacian Matrix ◽  
Group Differences ◽  
Algebraic Connectivity ◽  
Connected Graphs ◽  
Bicyclic Graph ◽  
Smallest Eigenvalue ◽  
Unique Graph ◽  
The Stability

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.

Problems on Graphs with Fixed Smallest Eigenvalue

2020 ◽  
Vol 27 (01) ◽  
pp. 51-54
Author(s):  
Jack Koolen ◽  
Qianqian Yang
Keyword(s):  
Smallest Eigenvalue

In this note we give several problems and conjectures on graphs with fixed smallest eigenvalue.

scholarly journals Domination number and Laplacian eigenvalue distribution

2016 ◽  
Vol 53 ◽  
pp. 66-71 ◽  
Author(s):  
Stephen T. Hedetniemi ◽  
David P. Jacobs ◽  
Vilmar Trevisan
Keyword(s):  
Domination Number ◽  
Eigenvalue Distribution ◽  
Laplacian Eigenvalue

scholarly journals A Novel similarity measure based on eigenvalue distribution

2016 ◽  
Vol 170 (3) ◽  
pp. 352-362 ◽  
Author(s):  
Xu Huang ◽  
Mansi Ghodsi ◽  
Hossein Hassani
Keyword(s):  
Similarity Measure ◽  
Eigenvalue Distribution
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