Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The distance matrix of a graph and its tree realization

Authors: A. N. Patrinos and S. L. Hakimi
Journal: Quart. Appl. Math. 30 (1972), 255-269
MSC: Primary 05C05
DOI: https://doi.org/10.1090/qam/414405
MathSciNet review: 414405
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Abstract: The results of Hakimi and Yau and others in the realization of a distance matrix are generalized to graphs (digraphs) whose branches (arcs) may have negative weights. Conditions under which such matrices have a tree, hypertree or directed tree realization are given, uniqueness of these realizations is discussed and algorithms for their construction are indicated.

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DOI: https://doi.org/10.1090/qam/414405
Article copyright: © Copyright 1972 American Mathematical Society

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