Ky Fan theorem applied to Randić energy
| Autor: | María Robbiano, Ivan Gutman, Enide Andrade Martins, Bernardo San Martín |
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| Rok vydání: | 2014 |
| Předmět: |
Ky Fan theorem
Numerical Analysis Algebra and Number Theory Randić matrix 010102 general mathematics 0211 other engineering and technologies Block matrix 021107 urban & regional planning 02 engineering and technology 01 natural sciences Square matrix Vertex (geometry) Combinatorics Matrix (mathematics) Singular value Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Normalized Laplacian matrix Randić energy Undirected graph Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 0024-3795 |
| Popis: | Let G be a simple undirected graph of order n with vertex set V ( G ) = { v 1 , v 2 , … , v n } . Let d i be the degree of the vertex v i . The Randic matrix R = ( r i , j ) of G is the square matrix of order n whose ( i , j ) -entry is equal to 1 / d i d j if the vertices v i and v j are adjacent, and zero otherwise. The Randic energy is the sum of the absolute values of the eigenvalues of R. Let X, Y, and Z be matrices, such that X + Y = Z . Ky Fan established an inequality between the sum of singular values of X, Y, and Z. We apply this inequality to obtain bounds on Randic energy. We also present results pertaining to the energy of a symmetric partitioned matrix, as well as an application to the coalescence of graphs. |
| Databáze: | OpenAIRE |
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