Generalized inverse of the Laplacian matrix and some applications
Generating potentially nilpotent full sign patterns.
Graph centers used for stabilization of matrix factorizations
Systems of consistent linear equations with symmetric positive semidefinite matrices arise naturally while solving many scientific and engineering problems. In case of a "floating" static structure, the boundary conditions are not sufficient to prevent its rigid body motions. Traditional solvers based on Cholesky decomposition can be adapted to these systems by recognition of zero rows or columns and also by setting up a well conditioned regular submatrix of the problem that...
Graph fibrations, graph isomorphism, and PageRank
PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...
Graphes de Ramanujan et applications
Graphes sans circuit et bilinéarité
Graphic matrices
Graphic Splitting of Cographic Matroids
In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
Graphs and their spectra
Graphs determined by their (signless) Laplacian spectra.
Graphs of diameter 2 with cyclic defect
Graphs whose energy does not exceed 3
Graphs whose minimal rank is two.
Graphs whose minimal rank is two: the finite fields case.
Graphs with given degree sequence and maximal spectral radius.
Graphs with least eigenvalue -2 attaining a convex quadratic upper bound for the stability number
Graphs with Least Eigenvalue at Least -sqrt(3)
Graphs with small diameter determined by their -spectra
Let be a connected graph with vertex set . The distance matrix is the matrix indexed by the vertices of , where denotes the distance between the vertices and . Suppose that are the distance spectrum of . The graph is said to be determined by its -spectrum if with respect to the distance matrix , any graph having the same spectrum as is isomorphic to . We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined...
Graphs with the Reduced Spectrum in the Unit Interval
Green functions on self-similar graphs and bounds for the spectrum of the laplacian
Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...