On Graphs with Exactly Three Q-main Eigenvalues
For a simple graph G, the Q-eigenvalues are the eigenvalues of the signless Laplacian matrix Q of G. A Q-eigenvalue is said to be a Q-main eigenvalue if it admits a corresponding eigenvector non orthogonal to the all-one vector, or alternatively if the sum of its component entries is non-zero. In th...
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Veröffentlicht in: | Filomat 2017-01, Vol.31 (6), p.1803-1812 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | For a simple graph G, the Q-eigenvalues are the eigenvalues of the signless Laplacian matrix Q of G. A Q-eigenvalue is said to be a Q-main eigenvalue if it admits a corresponding eigenvector non orthogonal to the all-one vector, or alternatively if the sum of its component entries is non-zero. In the literature the trees, unicyclic, bicyclic and tricyclic graphs with exactly two Q-main eigenvalues have been recently identified. In this paper we continue these investigations by identifying the trees with exactly three Q-main eigenvalues, where one of them is zero. |
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ISSN: | 0354-5180 2406-0933 |