Bounds for a alpha-eigenvalues

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aalpha(G), as a convex combination of A(G) and D(G), the following way, Aalpha(G) = alpha A(G) + (1 - alpha)D(G), where alpha belongs to [0,1]. In this paper, we present some new upper and lower bounds for the largest, second largest, and smallest eigenvalue of the Aalpha-matrix. Moreover, extremal graphs attaining some of these bounds are characterized


page 1

page 2

page 3

page 4


Some observations on the smallest adjacency eigenvalue of a graph

In this paper, we discuss various connections between the smallest eigen...

Observations on the Lovász θ-Function, Graph Capacity, Eigenvalues, and Strong Products

This paper provides new observations on the Lovász θ-function of graphs....

Support of Closed Walks and Second Eigenvalue Multiplicity of the Normalized Adjacency Matrix

We show that the multiplicity of the second normalized adjacency matrix ...

Bounds for the smallest k-chromatic graphs of given girth

Let n_g(k) denote the smallest order of a k-chromatic graph of girth at ...

Extreme singular values of inhomogeneous sparse random rectangular matrices

We develop a unified approach to bounding the largest and smallest singu...

Spectral Clustering Revisited: Information Hidden in the Fiedler Vector

We are interested in the clustering problem on graphs: it is known that ...

Optimality of Glauber dynamics for general-purpose Ising model sampling and free energy approximation

Recently, Eldan, Koehler, and Zeitouni (2020) showed that Glauber dynami...

Please sign up or login with your details

Forgot password? Click here to reset