scholarly journals On sum of powers of the Laplacian eigenvalues of graphs

2013 ◽  
Vol 439 (11) ◽  
pp. 3561-3575 ◽  
Author(s):  
Kinkar Ch. Das ◽  
Kexiang Xu ◽  
Muhuo Liu
Keyword(s):  
Laplacian Eigenvalues ◽  
Eigenvalues Of Graphs

On distance Laplacian and distance signless Laplacian eigenvalues of graphs

2018 ◽  
Vol 67 (11) ◽  
pp. 2307-2324 ◽  
Author(s):  
Kinkar Ch. Das ◽  
Mustapha Aouchiche ◽  
Pierre Hansen
Keyword(s):  
Laplacian Eigenvalues ◽  
Signless Laplacian ◽  
Eigenvalues Of Graphs

Distance signless Laplacian eigenvalues of graphs

2019 ◽  
Vol 14 (4) ◽  
pp. 693-713
Author(s):  
Kinkar Chandra Das ◽  
Huiqiu Lin ◽  
Jiming Guo
Keyword(s):  
Laplacian Eigenvalues ◽  
Signless Laplacian ◽  
Eigenvalues Of Graphs

On the sum of the distance signless Laplacian eigenvalues of a graph and some inequalities involving them

2019 ◽  
Vol 12 (01) ◽  
pp. 2050006 ◽  
Author(s):  
A. Alhevaz ◽  
M. Baghipur ◽  
E. Hashemi ◽  
S. Paul
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Simple Graph ◽  
Graph Invariants ◽  
Laplacian Eigenvalues ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Eigenvalues Of Graphs

The distance signless Laplacian matrix of a connected graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix of vertex transmissions of [Formula: see text]. If [Formula: see text] are the distance signless Laplacian eigenvalues of a simple graph [Formula: see text] of order [Formula: see text] then we put forward the graph invariants [Formula: see text] and [Formula: see text] for the sum of [Formula: see text]-largest and the sum of [Formula: see text]-smallest distance signless Laplacian eigenvalues of a graph [Formula: see text], respectively. We obtain lower bounds for the invariants [Formula: see text] and [Formula: see text]. Then, we present some inequalities between the vertex transmissions, distance eigenvalues, distance Laplacian eigenvalues, and distance signless Laplacian eigenvalues of graphs. Finally, we give some new results and bounds for the distance signless Laplacian energy of graphs.

LAPLACIAN EIGENVALUES OF GRAPHS WITH GIVEN DOMINATION NUMBER

2009 ◽  
Vol 02 (01) ◽  
pp. 71-76 ◽  
Author(s):  
Lihua Feng ◽  
Guihai Yu ◽  
Xiqin Lin
Keyword(s):  
Spectral Radius ◽  
Domination Number ◽  
Upper Bounds ◽  
Algebraic Connectivity ◽  
Laplacian Spectral Radius ◽  
Laplacian Eigenvalues ◽  
Eigenvalues Of Graphs

In this paper, we study the Laplacian eigenvalues of graphs on n vertices with domination number γ and present upper bounds for the Laplacian spectral radius and algebraic connectivity as well, which improve old results apparently.

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