This paper presents some upper and lower bounds on the greatest eigenvalue and a lower bound on the smallest eigenvalue.doi:10.1016/j.disc.2003.08.005Kinkar Ch. DasPawan KumarElsevier B.V.Discrete MathematicsSome new bounds on the spectral radius of graphs," in Discrete Mathematics, 2004....
Bounds on the greatest eigenvalue of graphs The eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents some upper bounds on the greatest eigenvalue of graphs and lowe... KC Das,P Kumar - 《Indian Journal of Pure & Applied Mathematics》 被引量: 29发表: 200...
Some new bounds on the spectral radius of graphs The eigenvalues of a graph are the eigenvalues of its adjacency matrix. This paper presents some upper and lower bounds on the greatest eigenvalue and a lo... KC Das,P Kumar - 《Discrete Mathematics》...
In this paper,based on the analysis of the structure of bipartite graphs,the characteristic of Laplacian matrices of bipartite graphs is studied,and the new bounds for the greatest eigenvalue of Laplacian matrices of bipartite graphs are given according to the theory of nonnegative matrices. 文章...
The greatest D -eigenvalue is called the D -spectral radius of G denoted by μ 1 . The D -energy E D ( G ) of the graph G is the sum of the absolute values of its D -eigenvalues. In this paper we obtain some lower bounds for μ 1 and characterize those graphs for which ...
1 we call a graph without isolated vertices -minimal if its th greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every ? 3 the path k on + 1 vertices is the unique -minimal graph....
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||𝒜||𝑜𝑝=𝜆(𝐺)(𝒜⊤𝒜)−−−−−−−−−−√||A||op=λ(G)(A⊤A), where 𝜆(𝐺)(𝒜⊤𝒜)λ(G)(A⊤A) denotes the greatest eigenvalue of 𝒜⊤𝒜A⊤A. Definition 1. An 𝑛×𝑛n×n matrix of the form 𝑐𝑖𝑟𝑐(𝑎0,...