Distance matrix from adjacency matrix using Hadamard product
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DOI:
https://doi.org/10.26637/MJM0803/0024Abstract
Distance matrix of a graph has important applications in the field of hierarchical clustering, phylogenetic analysis, bioinformatics, telecommunication etc. There are nice research works on determinant, characteristic polynomial and eigen values of distance matrices. This paper describes a formula for finding the distance matrix of a simple connected undirected graph from the powers of the adjacency matrix using Hadamard product on matrices.
Keywords:
Adjacency matrix, Distance matrix, Binary matrix, Diameter, Hadamard product, m-distance matrixMathematics Subject Classification:
Mathematics- Pages: 877-881
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
L. Graham and L. Lovasz, Distance matrix polynomials of trees, Advances in Mathematics, 29(1978), 60-88.
Bapat, Graphs and Matrices, Universitext, Springer, 2010.
Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, Courier Dover Publications, 2016.
F. Harary, Graph Theory, Addison-Wesley, 1994.
R. J. Wilson, Introduction to Graph Theory, 3rd ed. New York Lonoman 1985
Horn, A. Roger, Johnson, R. Charles, Matrix Analysis, Cambridge University Press, 2012.
M. Edelberg, M. R. Garey, and R. L. Graham, On the distance matrix of a tree, Discrete Mathematics, 14(1976), 23-39.
R. L. Graham and H. O. Pollak, On the addressing problem for loop switching, The Bell System Technical Journal, 50(1971), 2495-2519.
L. Graham and L. Lovasz, Distance matrix polynomials of trees, Advances in Mathematics, 29(1978), 60-88.
Bapat, Graphs and Matrices, Universitext, Springer, 2010.
Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, Courier Dover Publications, 2016.
F. Harary, Graph Theory, Addison-Wesley, 1994.
R. J. Wilson, Introduction to Graph Theory, 3rd ed. New York Lonoman 1985
Horn, A. Roger, Johnson, R. Charles, Matrix Analysis, Cambridge University Press, 2012.
M. Edelberg, M. R. Garey, and R. L. Graham, On the distance matrix of a tree, Discrete Mathematics, 14(1976), 23-39.
R. L. Graham and H. O. Pollak, On the addressing problem for loop switching, The Bell System Technical Journal, 50(1971), 2495-2519.
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