A characterization of singular graphs.
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A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
Kirkland, S. (2004)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A Fiedler-like theory for the perturbed Laplacian
Israel Rocha, Vilmar Trevisan (2016)
Czechoslovak Mathematical Journal
The perturbed Laplacian matrix of a graph is defined as , where is any diagonal matrix and is a weighted adjacency matrix of . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...
A formula for all minors of the adjacency matrix and an application
R. B. Bapat, A. K. Lal, S. Pati (2014)
Special Matrices
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.
A Generalization of the Matrix-Tree Theorem.
Mordechai Lewin (1982)
Mathematische Zeitschrift
A lower bound for the number of distinct eigenvalues of some real symmetric matrices.
Da Fonseca, C.M. (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A matrix representation of graphs and its spectrum as a graph invariant.
Emms, David, Hancock, Edwin R., Severini, Simone, Wilson, Richard C. (2006)
The Electronic Journal of Combinatorics [electronic only]
A multipartite version of the Turan problem - density conditions and eigenvalues.
Nagy, Zoltán Lóránt (2011)
The Electronic Journal of Combinatorics [electronic only]
A necessary and sufficient eigenvector condition for a connected graph to be bipartite.
Cioaba, Sebastian M. (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A new determinant expression of the zeta function for a hypergraph.
Sato, Iwao (2009)
The Electronic Journal of Combinatorics [electronic only]
A new like quantity based on “Estrada index”.
Güngör, A.Dilek (2010)
Journal of Inequalities and Applications [electronic only]
A new spectral method for determining the number of spanning trees.
Cvetkovic, D.M., Gutman, I. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
A new upper bound for the Laplacian spectral radius of a graph.
Yu, Aimei (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A note on a distance bound using eigenvalues of the normalized Laplacian matrix.
Kirkland, Steve (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A Note On Analogies Between Characteristic And The Matching Polynomial Of A Graph
Ivan Gutman (1982)
Publications de l'Institut Mathématique
A Note On Constructions Of Graphs By Means Of Their Spectra
Dragoš M. Cvetković (1980)
Publications de l'Institut Mathématique
A note on graphs with two main eigenvalues
Mirko Lepović (2002)
Kragujevac Journal of Mathematics
A note on linear discrepancy.
Dahl, Geir (2003)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A note on minimum rank and maximum nullity of sign patterns.
Hogben, Leslie (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A note on the largest eigenvalue of non-regular graphs.
Liu, Bolian, Li, Gang (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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