The Sharp Upper Bounds on the $$A_{\alpha }$$-Spectral Radius of $$C_4$$-Free Graphs and Halin Graphs

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Shu-Guang Guo ◽  
Rong Zhang
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Halin Graphs

scholarly journals Upper bounds for the signless Laplacian spectral radius of graphs on surfaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3473-3481
Author(s):  
Xiaodan Chen ◽  
Yaoping Hou
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Outerplanar Graphs ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Graphs On Surfaces ◽  
Halin Graphs

In this paper, we present some new upper bounds for the signless Laplacian spectral radius of graphs embeddable on a fixed surface, which improve several previously known results. We also give several improved upper bounds for the signless Laplacian spectral radius of outerplanar graphs and Halin graphs.

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

scholarly journals On Numerical Radius of a Matrix and Estimation of Bounds for Zeros of a Polynomial

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Kallol Paul ◽  
Santanu Bag
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Numerical Radius ◽  
Bounds For Zeros

We obtain inequalities involving numerical radius of a matrixA∈Mn(ℂ). Using this result, we find upper bounds for zeros of a given polynomial. We also give a method to estimate the spectral radius of a given matrixA∈Mn(ℂ)up to the desired degree of accuracy.

scholarly journals Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Houqing Zhou ◽  
Youzhuan Xu
Keyword(s):  
Spectral Radius ◽  
Transient Stability ◽  
Laplacian Matrix ◽  
Schwarz Inequality ◽  
Upper Bounds ◽  
Power Network ◽  
Laplacian Eigenvalue ◽  
Laplacian Spectral Radius ◽  
Wide Range ◽  
Simple Connected Graph

The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power network to distributed control of formations. LetG=(V,E)be a simple connected graph onnvertices and letμ(G)be the largest Laplacian eigenvalue (i.e., the spectral radius) ofG. In this paper, by using the Cauchy-Schwarz inequality, we show that the upper bounds for the Laplacian spectral radius ofG.

scholarly journals The Spectral Radius for a Class of Double-Star-Like Tree Systems with Maximal Degree 4

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yufeng Mao ◽  
Meijin Xu ◽  
Xiaodong Chen ◽  
Yan-Jun Liu ◽  
Kai Li
Keyword(s):  
Spectral Radius ◽  
Transformation Method ◽  
Upper Bounds ◽  
Double Star ◽  
Maximal Degree ◽  
Extremal Graphs ◽  
Second Degree

We mainly study the properties of the 4-double-star-like tree, which is the generalization of star-like trees. Firstly we use graft transformation method to obtain the maximal and minimum extremal graphs of 4-double-star-like trees. Secondly, by the relations between the degree and second degree of vertices in maximal extremal graphs of 4-double-star-like trees we get the upper bounds of spectral radius of 4-double-star-like trees.

scholarly journals Sharp upper bounds on the distance spectral radius of a graph

2013 ◽  
Vol 439 (9) ◽  
pp. 2659-2666 ◽  
Author(s):  
Yingying Chen ◽  
Huiqiu Lin ◽  
Jinlong Shu
Keyword(s):  
Spectral Radius ◽  
Upper Bounds

TWO SHARP UPPER BOUNDS FOR THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS

2011 ◽  
Vol 03 (02) ◽  
pp. 185-191 ◽  
Author(s):  
YA-HONG CHEN ◽  
RONG-YING PAN ◽  
XIAO-DONG ZHANG
Keyword(s):  
Spectral Radius ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Upper Bounds ◽  
Extremal Graphs ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Matrix ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

The signless Laplacian matrix of a graph is the sum of its degree diagonal and adjacency matrices. In this paper, we present a sharp upper bound for the spectral radius of the adjacency matrix of a graph. Then this result and other known results are used to obtain two new sharp upper bounds for the signless Laplacian spectral radius. Moreover, the extremal graphs which attain an upper bound are characterized.

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