A characterization of singular graphs.
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A Fiedler-like theory for the perturbed Laplacian
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
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.
A lower bound for the number of distinct eigenvalues of some real symmetric matrices.
A matrix representation of graphs and its spectrum as a graph invariant.
A multipartite version of the Turan problem - density conditions and eigenvalues.
A necessary and sufficient eigenvector condition for a connected graph to be bipartite.
A new determinant expression of the zeta function for a hypergraph.
A new like quantity based on “Estrada index”.
A new spectral method for determining the number of spanning trees.
A new upper bound for the Laplacian spectral radius of a graph.
A note on a distance bound using eigenvalues of the normalized Laplacian matrix.
A Note On Analogies Between Characteristic And The Matching Polynomial Of A Graph
A Note On Constructions Of Graphs By Means Of Their Spectra
A note on graphs with two main eigenvalues
A note on linear discrepancy.
A note on minimum rank and maximum nullity of sign patterns.
A note on the largest eigenvalue of non-regular graphs.