scholarly journals An efficient lower bound for the generalized spectral radius of a set of matrices

1996 ◽  
Vol 240 ◽  
pp. 1-7 ◽  
Author(s):  
Mohsen Maesumi
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Generalized Spectral Radius

scholarly journals A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter

2008 ◽  
Author(s):  
Sebastian Cioaba ◽  
Edwin van Dam ◽  
Jack Koolen ◽  
Jae-Ho Lee
Keyword(s):  
Lower Bound ◽  
Spectral Radius

scholarly journals New Bounds for the α-Indices of Graphs

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1668
Author(s):  
Eber Lenes ◽  
Exequiel Mallea-Zepeda ◽  
Jonnathan Rodríguez
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Independence Number ◽  
Minimal Degree ◽  
Diagonal Matrix ◽  
The Matrix

Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G. This paper presents some extremal results about the spectral radius ρα(G) of the matrix Aα(G). In particular, we give a lower bound on the spectral radius ρα(G) in terms of order and independence number. In addition, we obtain an upper bound for the spectral radius ρα(G) in terms of order and minimal degree. Furthermore, for n>l>0 and 1≤p≤⌊n−l2⌋, let Gp≅Kl∨(Kp∪Kn−p−l) be the graph obtained from the graphs Kl and Kp∪Kn−p−l and edges connecting each vertex of Kl with every vertex of Kp∪Kn−p−l. We prove that ρα(Gp+1)<ρα(Gp) for 1≤p≤⌊n−l2⌋−1.

scholarly journals Cauchy's interlace theorem and lower bounds for the spectral radius

2000 ◽  
Vol 23 (8) ◽  
pp. 563-566 ◽  
Author(s):  
A. McD. Mercer ◽  
Peter R. Mercer
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Lower Bounds ◽  
Simple Proof ◽  
Symmetric Matrix ◽  
Real Symmetric Matrix

We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.

scholarly journals A lower bound for the spectral radius of graphs with fixed diameter

2010 ◽  
Vol 31 (6) ◽  
pp. 1560-1566 ◽  
Author(s):  
Sebastian M. Cioabă ◽  
Edwin R. van Dam ◽  
Jack H. Koolen ◽  
Jae-Ho Lee
Keyword(s):  
Lower Bound ◽  
Spectral Radius
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