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The distance matrix in chemistry
Journal of Mathematical Chemistry, 1992The graph-theoretical (topological) distance matrix and the geometric (topographic) distance matrix and their invariants (polynomials, spectra, determinants and Wiener numbers) are presented. Methods of computing these quantities are discussed. The uses of the distance matrix in both forms and the related invariants in chemistry are surveyed.
Zlatko Mihalić +2 more
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Journal of Computational Chemistry, 2010
AbstractWe have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n‐dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n‐dimensional space.
Milan Randic +2 more
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AbstractWe have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n‐dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n‐dimensional space.
Milan Randic +2 more
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The Euclidian Distance Matrix Completion Problem
SIAM Journal on Matrix Analysis and Applications, 1995Motivated by the molecular mapping (or ``conformation'') problem, i.e., the problem of deducing the possible shapes of a molecule from partial (or inaccurate) information about interatomic distances, the authors study the completions of partial Euclidean distance matrices, i.e., the choice of values for each of the unspecified entries, resulting in a ...
Mihály Bakonyi
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The exponential distance matrix of block graphs
Applied Mathematics and Computation, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhibin Du
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Nearest Neighbour Distance Matrix Classification
, 2010 A distance based classification is one of the popular methods for classifying instances using a point-to-point distance based on the nearest neighbour or k-NEAREST NEIGHBOUR (k-NN). The representation of distance measure can be one of the various measures available (e.g.
Mohd Shamrie Sainin, Rayner Alfred
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The distance matrix of caterpillar
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joice S. do Nascimento +2 more
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Topological energy of the distance matrix
Communications in Nonlinear Science and Numerical Simulation, 2022This paper deals with the energy and entropy of a graph. Using the distance matrix the authors defined a graph sequence. They calculated the average in the appropriate interval to get the definition of the topological energy of the distance matrix. This method is explained in Section 3.
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On the distance matrix of a directed graph
Journal of Graph Theory, 1977AbstractIn this note, we show how the determinant of the distance matrix D(G) of a weighted, directed graph G can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks Gi of G. In particular, when cof D(G), the sum of the cofactors of D(G), does not vanish, we have the very attractive formulamagnified image.
Ronald L. Graham +2 more
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Preconditioners for distance matrix algorithms
Journal of Computational Chemistry, 1994AbstractA recent gradient algorithm in nonlinear optimization uses a novel idea that avoids line searches. This so‐called spectral gradient algorithm works well when the spectrum of the Hessian of the function to be minimized has a small range or is clustered. In this article, we find a general preconditioning method for this algorithm.
William Kile Glunt +2 more
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