Corpus ID: 235458590

On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

@inproceedings{Wang2021OnTS,
  title={On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter},
  author={F. F. Wang and H. Shan and Y. Zhai},
  year={2021}
}
The α-spectral radius of a connected graph G is the spectral radius of Aα-matrix of G. In this paper, we discuss the methods for comparing α-spectral radius of graphs. As applications, we characterize the graphs with the maximal α-spectral radius among all unicyclic and bicyclic graphs of order n with diameter d, respectively. Finally, we determine the unique graph with maximal signless Laplacian spectral radius among bicyclic graphs of order n with diameter d. From our conclusion, it is known… Expand

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SHOWING 1-10 OF 20 REFERENCES
On the spectral radius of bicyclic graphs with n vertices and diameter d
Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. In this paper we determine the graph with the largest spectral radius among all bicyclicExpand
On the Aα-spectral radius of a graph
Abstract Let G be a graph with adjacency matrix A ( G ) and let D ( G ) be the diagonal matrix of the degrees of G. For any real α ∈ [ 0 , 1 ] , Nikiforov [3] defined the matrix A α ( G ) as A α ( GExpand
The Aα-spectral radius of trees and unicyclic graphs with given degree sequence
TLDR
It is shown that the greedy tree has the maximum Aα-spectral radius in G D when D is a tree degree sequence firstly. Expand
On the spectral radius of tricyclic graphs with a fixed diameter
A tricyclic graph is a connected graph with n vertices and n + 2 edges. In this article, we determine graphs with the largest spectral radius among the n-vertex tricyclic graphs with given diameter d.
On the α-index of graphs with pendent paths
Abstract Let G be a graph with adjacency matrix A ( G ) and let D ( G ) be the diagonal matrix of the degrees of G. For every real α ∈ [ 0 , 1 ] , write A α ( G ) for the matrix A α ( G ) = α D ( G )Expand
On the spectral radius of unicyclic graphs with fixed diameter
In the paper, we will determine graphs with the maximal spectral radius among all the unicyclic graphs with n vertices and diameter d.
On the Spectral Radius of Trees With n Vertices and Diameter d
Eigenvalues of bipartite graphs have significance in quantum chemistry. Therefore it is of great practical value to study the eigenvalues of bipartite graphs. Denote by Pd+1("d+2/2",n-d-1) andExpand
On the signless Laplacian index of unicyclic graphs with fixed diameter
Abstract In the paper, we identify graphs with the maximal signless Laplacian spectral radius among all the unicyclicgraphs with n vertices of diameter d .
Combinatorial approach for computing the characteristic polynomial of a matrix
The study of the spectrum of weighted (di)graphs has attracted recently much attention in the literature. Here we use the Coates digraph as a main tool to extend, in a combinatorial way, some wellExpand
On the Spectral Radius of (0, 1)-Matrices with 1's in Prescribed Positions
TLDR
This work investigates the maximum and minimum spectral radii of a $(0,1)-matrix of order $n$ that has 1 on and below its main diagonal and additional 1's and proves an asymptotic result that severely limits the structure of matrices with maximum spectral radius. Expand
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