Geodesic
Smith normal form and acyclic matrices
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 63-80.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree $T$) is related to the maximal multiplicity $MaxMult( T)$ occurring for an eigenvalue of a symmetric matrix whose graph is $T$ (resp. the minimal number $q( T)$ of distinct eigenvalues over the symmetric matrices whose graphs are $T$). The approach is also applied to a more general class of connected graphs $G$, not necessarily trees, in order to establish a lower bound on $q( G)$.
Keywords: keywords Smith normal form, acyclic matrix, graph spectra 
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     title = {Smith normal form and acyclic matrices},
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Kim, In-Jae; Shader, Bryan L. Smith normal form and acyclic matrices. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 63-80. http://geodesic.mathdoc.fr/item/JAC_2009__29_1_a3/