Ela on Euclidean Distance Matrices of Graphs

Ela Euclidean and Circum-euclidean Distance Matrices: Characterizations and Linear Preservers

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

Ela Block Distance Matrices

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D ij = F ii +F jj −2F ij. When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interes...

Ela Matrices and Graphs in Euclidean Geometry

Some examples of the interplay between matrix theory, graph theory and n-dimensional Euclidean geometry are presented. In particular, qualitative properties of interior angles in simplices are completely characterized. For right simplices, a relationship between the tree of legs and the circumscribed Steiner ellipsoids is proved.

Ela Jacobi Matrices and Boundary Value Problems in Distance-regular Graphs

Regular boundary value problems on a distance-regular graph associated with Schrödinger operators are analyzed. These problems include the cases in which the boundary has one or two vertices. In each case, the Green matrices are given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graphs.

On Euclidean distance matrices of graphs