It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l
AbstractA graph describes the zero–nonzero pattern of a family of matrices, with the type of graph (...
AbstractSuppose A is an invertible sign symmetric matrix whose associated digraph D(A) is a tree. Th...
AbstractThe algorithm we present is a natural next step to well-known algorithms for finding optimal...
Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact ...
Let T be a tree, let S(T) denote the set of real symmetric matrices whose graph is T, and let U(T) b...
AbstractA sign pattern is a matrix whose entries are elements of {+,−,0}; it describes the set of re...
By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general sym...
AbstractAmong those real symmetric matrices whose graph is a given tree T, the maximum multiplicity ...
AbstractLet T denote a tree with at least three vertices. Observe that T contains a vertex which has...
The set of real matrices described by a sign pattern (a matrix whose entries are elements of {+,−, 0...
Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T c...
Tree-width, and variants that restrict the allowable tree decompositions, play an important role in ...
Abstract There is remarkable and distinctive structure among Hermitian matrices, whose graph is a gi...
Abstract. For a given graph G we consider a set S(G) of all symmetric matrices A = [aij] whose nonze...
AbstractThe symmetric M-matrix and symmetric M0-matrix completion problems are solved and results of...
AbstractA graph describes the zero–nonzero pattern of a family of matrices, with the type of graph (...
AbstractSuppose A is an invertible sign symmetric matrix whose associated digraph D(A) is a tree. Th...
AbstractThe algorithm we present is a natural next step to well-known algorithms for finding optimal...
Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact ...
Let T be a tree, let S(T) denote the set of real symmetric matrices whose graph is T, and let U(T) b...
AbstractA sign pattern is a matrix whose entries are elements of {+,−,0}; it describes the set of re...
By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general sym...
AbstractAmong those real symmetric matrices whose graph is a given tree T, the maximum multiplicity ...
AbstractLet T denote a tree with at least three vertices. Observe that T contains a vertex which has...
The set of real matrices described by a sign pattern (a matrix whose entries are elements of {+,−, 0...
Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T c...
Tree-width, and variants that restrict the allowable tree decompositions, play an important role in ...
Abstract There is remarkable and distinctive structure among Hermitian matrices, whose graph is a gi...
Abstract. For a given graph G we consider a set S(G) of all symmetric matrices A = [aij] whose nonze...
AbstractThe symmetric M-matrix and symmetric M0-matrix completion problems are solved and results of...
AbstractA graph describes the zero–nonzero pattern of a family of matrices, with the type of graph (...
AbstractSuppose A is an invertible sign symmetric matrix whose associated digraph D(A) is a tree. Th...
AbstractThe algorithm we present is a natural next step to well-known algorithms for finding optimal...
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