scholarly journals On the maximum number of maximum independent sets in connected graphs

2020 ◽  
Author(s):  
Elena Mohr ◽  
Dieter Rautenbach
Keyword(s):  
Independent Sets ◽  
Connected Graphs

Independent sets in n-vertex k-chromatic ℓ-connected graphs

2021 ◽  
Vol 344 (7) ◽  
pp. 112376
Author(s):  
John Engbers ◽  
Lauren Keough ◽  
Taylor Short
Keyword(s):  
Independent Sets ◽  
Connected Graphs

scholarly journals The maximum number of maximal independent sets in unicyclic connected graphs

2008 ◽  
Vol 308 (17) ◽  
pp. 3761-3769 ◽  
Author(s):  
K.M. Koh ◽  
C.Y. Goh ◽  
F.M. Dong
Keyword(s):  
Independent Sets ◽  
Connected Graphs ◽  
Maximal Independent Sets

scholarly journals CONNECTED GRAPHS WITH A LARGE NUMBER OF INDEPENDENT SETS

2013 ◽  
Vol 17 (6) ◽  
pp. 2011-2017
Author(s):  
Min-Jen Jou
Keyword(s):  
Independent Sets ◽  
Connected Graphs

scholarly journals Finding Independent Sets inK4-Free 4-Regular Connected Graphs

1997 ◽  
Vol 71 (1) ◽  
pp. 85-110 ◽  
Author(s):  
Stephen C. Locke ◽  
Feng Lou
Keyword(s):  
Independent Sets ◽  
Connected Graphs

scholarly journals The Formula to Count The Number of Vertices Labeled Order Six Connected Graphs with Maximum Thirty Edges without Loops

2021 ◽  
Vol 1751 ◽  
pp. 012023
Author(s):  
F C Puri ◽  
Wamiliana ◽  
M Usman ◽  
Amanto ◽  
M Ansori ◽  
...  
Keyword(s):  
Connected Graphs

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.

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