منابع مشابه
Unicyclic graphs with exactly two main eigenvalues
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero, and it is well known that a graph has exactly one main eigenvalue if and only if it is regular. In this work, all connected unicyclic graphs with exactly two main eigenvalues are determined. c © 2006 Elsevier Ltd. All rights reserved.
متن کاملOrdering Unicyclic Graphs in Terms of Their Smaller Least Eigenvalues
Let G be a simple graph with n vertices, and let A be the 0, 1 -adjacency matrix of G. We call det λI −A the characteristic polynomial of G, denoted by P G; λ , or abbreviated P G . Since A is symmetric, its eigenvalues λ1 G , λ2 G , . . . , λn G are real, and we assume that λ1 G ≥ λ2 G ≥ · · · ≥ λn G . We call λn G the least eigenvalue of G. Up to now, some good results on the least eigenvalue...
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If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2017
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm1702273b