scholarly journals Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs

2020 ◽  
Vol 40 (2) ◽  
pp. 417 ◽  
Author(s):  
Francesco Belardo ◽  
Maurizzo Brunetti ◽  
Nathan Reff
Keyword(s):  
Laplacian Eigenvalue ◽  
Gain Graphs

Glossary of Signed and Gain Graphs

10.37236/31 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
Thomas Zaslavsky
Keyword(s):  
Gain Graphs

A glossary to accompany DS8.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance 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

On signed graphs whose second largest Laplacian eigenvalue does not exceed 3

2015 ◽  
Vol 64 (9) ◽  
pp. 1785-1799 ◽  
Author(s):  
Francesco Belardo ◽  
Paweł Petecki ◽  
Jianfeng Wang
Keyword(s):  
Signed Graphs ◽  
Laplacian 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 Acceleration of Weak Galerkin Methods for the Laplacian Eigenvalue Problem

2018 ◽  
Vol 79 (2) ◽  
pp. 914-934
Author(s):  
Qilong Zhai ◽  
Hehu Xie ◽  
Ran Zhang ◽  
Zhimin Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Methods ◽  
Weak Galerkin ◽  
Laplacian Eigenvalue
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