Main Q-eigenvalues and generalized Q-cospectrality of graphs

Tianyi Bu, Lizhu Sun, Wenzhe Wang and Jiang Zhou ()
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Tianyi Bu: Harbin Engineering University
Lizhu Sun: Harbin Engineering University
Wenzhe Wang: Harbin Engineering University
Jiang Zhou: Harbin Engineering University

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 4, 531-538

Abstract: Abstract Let Q G denote the signless Laplacian matrix of a graph G. An eigenvalue μ of Q G is said to be a main Q-eigenvalue of G if μ has an eigenvector which is not orthogonal to an all-ones vector e. We give some basic properties of main Q-eigenvalues. For a graph G of order n, G is called Q-controllable if G has n distinct main Q-eigenvalues. We show that a graph H is generalized Q-cospectral with a Q-controllable G if and only if H is Q-controllable and there exists a unique rational orthogonal matrix R such that R e = e, Q H = R ⊤ Q G R.

Keywords: Signless Laplacian matrix; main Q-eigenvalue; cospectral graphs (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0079-2

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