The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
The resultant of non-commutative polynomials
The ring of invariants of three -matrices over a field of prime characteristic.
The ring of upper triangular invariants as a module over the Dickson invariants.
The Robson cubics for matrix algebras with involution.
The scattering matrix of a graph.
The semigroup of circulant Boolean matrices
The semigroup of fully indecomposable relations and Hall relations
The Sherman-Morrison formula and eigenvalues of a special bordered matrix.
The signless Laplacian separator of graphs.
The signless Laplacian spectral radius of graphs with given number of cut vertices
In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
The Similarity Reduction of Matrices over a Skew Field.
The Singular Values of Involutory and of Idempotent Matrices.
The singularity/nonsingularity problem for matrices satisfying diagonal dominance conditions formulated in terms of directed graphs.
The Smith normal form of product distance matrices
Let G = (V, E) be a connected graph with 2-connected blocks H1, H2, . . . , Hr. Motivated by the exponential distance matrix, Bapat and Sivasubramanian in [4] defined its product distance matrix DG and showed that det DG only depends on det DHi for 1 ≤ i ≤ r and not on the manner in which its blocks are connected. In this work, when distances are symmetric, we generalize this result to the Smith Normal Form of DG and give an explicit formula for the invariant factors of DG.
The special circulant matrix and units in group rings.
The spectral gap of random graphs with given expected degrees.
The spectral laws of Hermitian block-matrices with large random blocks.
The spectral radii of an operator and its modulus
The spectral radius and the maximum degree of irregular graphs.