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2008, br. 12-1, str. 111-116
The main eigenvalues of the Seidel matrix
(naslov ne postoji na srpskom)
Department of Mathematics, Shaoyang University, Hunan, P.R. China

Ključne reči: graph spectra; main eigenvalues; Seidel matrix
Sažetak
(ne postoji na srpskom)
Let G be a simple graph with vertex set V (G) and (0, 1)-adjacency matrix A. As usual, A*(G) = J - I - 2A denotes the Seidel matrix of the graph G. The eigenvalue λ of A is said to be a main eigenvalue of G if the eigenspace ε(λ) is not orthogonal to the all-1 vector e. In this paper, relations between the main eigenvalues and associated eigenvectors of adjacency matrix and Seidel matrix of a graph are investigated.
 Reference Cvetković, D.M., Doob, M., Sachs, H. (1995) Spectra of graphs: Theory and application. Heidelberg-Leipzig: Barth Verlag Cvetković, D.M., Doob, M. (1985) Developments in the theory of graph spectra. Linear and Multilinear Algebra, 18, 2, 153-181 Cvetković, D.M., Rowlinson, P., Simić, S.K. (1997) Eigenspaces of graphs. u: Encyclopedia of Mathematics and its Applications, Cambridge, itd: Cambridge University Press / CUP, vol. 66 Hagos, E.M. (2002) Some results on graph spectra. Linear Algebra Appl, 356, 103-111 Hou, P.Y., Zhou, Q.H. (2005) Trees with exactly two main eigenvalues. J Nat. Sci. Hunan Norm. Univ, 26, 1-3 Lepović, M.V. (2002) A note on graph with two main eigenvalues. Kragujevac Journal of Mathematics, br. 24, str. 42-53 Lepović, M.V. (2003) On the seidel eigenvectors of a graph. Publikacija Elektrotehničkog fakulteta - serija: matematika, br. 14, str. 4-10 Rowlinson, P. (2007) The main eigenvalues of a graph: A survey. Applicable Analysis and Discrete Mathematics, vol. 1, br. 2, str. 455-471 Seidel, J.J. (1968) Strongly regular graphs with (−1, 0, 1)-adjacency matrix have eigenvalue 3. Linear Algebra and Its Applications, 1, 281-298

## O članku

DOI: 10.5937/MatMor0801111Z
objavljen u SCIndeksu: 02.02.2009.

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