Abstract
A graph G is called a binary Hamming graph if each vertex of G can be assigned a binary address of fixed length such that the Hamming distance between two addresses equals the length of a shortest path in G between the corresponding vertices.
It is shown that O(n 2 log n) time and O(n 2) space suffices for deciding whether an n-vertex graph G is a binary Hamming graph, and for computing a binary addressing scheme for G provided its existence. This is not far from being optimal since the addressing scheme may require O(n 2) space.
This work was done while the first author was at IIG, Technische Universität Graz.
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© 1991 Springer-Verlag Berlin Heidelberg
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Aurenhammer, F., Hagauer, J. (1991). Recognizing binary hamming graphs in O(n 2 log n) time. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_34
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DOI: https://doi.org/10.1007/3-540-53832-1_34
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