scholarly journals Characterization of extremal graphs from distance signless Laplacian eigenvalues

2016 ◽  
Vol 500 ◽  
pp. 77-87 ◽  
Author(s):  
Huiqiu Lin ◽  
Kinkar Ch. Das
Keyword(s):  
Extremal Graphs ◽  
Laplacian Eigenvalues ◽  
Signless Laplacian

scholarly journals Extremal graphs for the sum of the two largest signless Laplacian eigenvalues

2015 ◽  
Vol 30 ◽  
pp. 605-612 ◽  
Author(s):  
Carla Oliveira ◽  
Leonado Lima ◽  
Paula Rama ◽  
Paula Carvalho
Keyword(s):  
Adjacency Matrix ◽  
Simple Graph ◽  
Diagonal Matrix ◽  
Star Graph ◽  
Extremal Graphs ◽  
Laplacian Eigenvalues ◽  
Signless Laplacian ◽  
Additional Edge ◽  
Largest Eigenvalues

Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q_1(G) and q_2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S_n^+ the star graph with an additional edge. It is proved that inequality q_1(G)+q_2(G) \leq e(G)+3 is tighter for the graph S_n^+ among all firefly graphs and also tighter to S_n^+ than to the graphs K_k \vee K_{n−k} recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S_n^+ minimizes f(G) = e(G) − q_1(G) − q_2(G) among all graphs G on n vertices.

scholarly journals On the sum of signless Laplacian eigenvalues of a graph

2013 ◽  
Vol 438 (11) ◽  
pp. 4539-4546 ◽  
Author(s):  
F. Ashraf ◽  
G.R. Omidi ◽  
B. Tayfeh-Rezaie
Keyword(s):  
Laplacian Eigenvalues ◽  
Signless Laplacian

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

scholarly journals Bounds for the Generalized Distance Eigenvalues of a Graph

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1529 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal Ahmad Ganie ◽  
Yilun Shang
Keyword(s):  
Spectral Radius ◽  
Undirected Graph ◽  
Minimum Degree ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Extremal Graphs ◽  
Special Cases ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Generalized Distance

Let G be a simple undirected graph containing n vertices. Assume G is connected. Let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian, D Q ( G ) be the distance signless Laplacian, and T r ( G ) be the diagonal matrix of the vertex transmissions, respectively. Furthermore, we denote by D α ( G ) the generalized distance matrix, i.e., D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where α ∈ [ 0 , 1 ] . In this paper, we establish some new sharp bounds for the generalized distance spectral radius of G, making use of some graph parameters like the order n, the diameter, the minimum degree, the second minimum degree, the transmission degree, the second transmission degree and the parameter α , improving some bounds recently given in the literature. We also characterize the extremal graphs attaining these bounds. As an special cases of our results, we will be able to cover some of the bounds recently given in the literature for the case of distance matrix and distance signless Laplacian matrix. We also obtain new bounds for the k-th generalized distance eigenvalue.

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
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