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CLASSIFICATION OF TREES EACH OF WHOSE ASSOCIATED ACYCLIC MATRICES WITH DISTINCT DIAGONAL ENTRIES HAS DISTINCT EIGENVALUES
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 Title & Authors
CLASSIFICATION OF TREES EACH OF WHOSE ASSOCIATED ACYCLIC MATRICES WITH DISTINCT DIAGONAL ENTRIES HAS DISTINCT EIGENVALUES
Kim, In-Jae; Shader, Bryan L.;
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 Abstract
It is known that each eigenvalue of a real symmetric, irreducible, tridiagonal matrix has multiplicity 1. The graph of such a matrix is a path. In this paper, we extend the result by classifying those trees for which each of the associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct.
 Keywords
acyclic matrix;Parter-vertex;simple eigenvalue;
 Language
English
 Cited by
1.
The maximum number of P-vertices of some nonsingular double star matrices, Discrete Mathematics, 2013, 313, 20, 2192  crossref(new windwow)
2.
Nonsingular acyclic matrices with full number of P-vertices, Linear and Multilinear Algebra, 2013, 61, 1, 49  crossref(new windwow)
 References
1.
A. Leal Duarte and C. R. Johnson, On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree, Math. Inequal. Appl. 5 (2002), no. 2, 175-180

2.
C. Godsil and G. Royle, Algebraic graph theory, Graduate Texts in Mathematics, 207. Springer-Verlag, New York, 2001

3.
R. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, Cambridge, 1985

4.
C. R. Johnson and A. Leal Duarte, The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, Linear and Multilinear Algebra 46 (1999), no. 1-2, 139-144 crossref(new window)

5.
C. R. Johnson, A. Leal Duarte, and C. M. Saiago, The Parter-Wiener theorem: refinement and generalization, SIAM J. Matrix Anal. Appl. 25 (2003), no. 2, 352-361 crossref(new window)