A note on the second largest eigenvalue of the laplacian matrix of a graph∗

2000 ◽  
Vol 48 (2) ◽  
pp. 117-121 ◽  
Author(s):  
Jiong-Sheng Li ◽  
Yong-Liang Pan
Keyword(s):  
Laplacian Matrix ◽  
Largest Eigenvalue ◽  
Second Largest Eigenvalue

Graphs with the second signless Laplacian eigenvalue ≤ 4

2021 ◽  
Vol 10 (1) ◽  
pp. 131-152
Author(s):  
Stephen Drury
Keyword(s):  
General Solution ◽  
Knapsack Problem ◽  
Laplacian Eigenvalue ◽  
Simple Graphs ◽  
Largest Eigenvalue ◽  
Signless Laplacian ◽  
Second Largest Eigenvalue

Abstract We discuss the question of classifying the connected simple graphs H for which the second largest eigenvalue of the signless Laplacian Q(H) is ≤ 4. We discover that the question is inextricable linked to a knapsack problem with infinitely many allowed weights. We take the first few steps towards the general solution. We prove that this class of graphs is minor closed.

scholarly journals The Laplacian Spread of Tricyclic Graphs

10.37236/169 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Yanqing Chen ◽  
Ligong Wang
Keyword(s):  
Laplacian Matrix ◽  
Largest Eigenvalue ◽  
Smallest Eigenvalue ◽  
Fixed Order ◽  
Tricyclic Graphs ◽  
The Difference ◽  
The Largest Eigenvalue

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order.

On the estimation of the second largest eigenvalue of Markov ciphers

2016 ◽  
pp. n/a-n/a
Author(s):  
Weijia Xue ◽  
Tingting Lin ◽  
Xin Shun ◽  
Fenglei Xue ◽  
Xuejia Lai
Keyword(s):  
Largest Eigenvalue ◽  
Second Largest Eigenvalue

scholarly journals On graphs whose second largest eigenvalue does not exceed (√5−1)2

1995 ◽  
Vol 138 (1-3) ◽  
pp. 213-227 ◽  
Author(s):  
Dragoš Cvetković ◽  
Slobodan Simić
Keyword(s):  
Largest Eigenvalue ◽  
Second Largest Eigenvalue

scholarly journals Evaluation of the Efficacy of Cancer Drugs by Using the Second Largest Eigenvalue of Metabolic Cancer Pathways

2018 ◽  
Vol 11 (3) ◽  
Author(s):  
Drasko Tomic ◽  
Karolj Skala ◽  
Lado Kranjcevic ◽  
Boris Pirkic ◽  
Sanja Stifter ◽  
...  
Keyword(s):  
Cancer Drugs ◽  
Largest Eigenvalue ◽  
Cancer Pathways ◽  
Second Largest Eigenvalue
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