Distance spectra of graphs: A survey
In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Sinc...
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| Published in | Linear algebra and its applications Vol. 458; pp. 301 - 386 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.10.2014
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties. |
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| AbstractList | In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties. |
| Author | Aouchiche, Mustapha Hansen, Pierre |
| Author_xml | – sequence: 1 givenname: Mustapha surname: Aouchiche fullname: Aouchiche, Mustapha email: mustapha.aouchiche@gerad.ca – sequence: 2 givenname: Pierre surname: Hansen fullname: Hansen, Pierre email: pierre.hansen@gerad.ca |
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