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The relation graph
Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North, New Zealand.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2002 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 244, no 1-3, 153-166 p.Article in journal (Refereed) Published
Abstract [en]

Given a set R of distinct, non-trivial partitions of a finite set, we define the relation graph G(R) of R. In case R consists only of bipartitions, G(R) is the well-known Buneman graph, a median graph that has applications in the area of phylogenetic analysis., Here we consider properties of the relation graph for general sets of partitions and, in particular, we see that it mimics the behaviour of the Buneman graph by proving the following two theorems:(i) The graph G(R) is a Hamming graph if and only if R is strongly incompatible.(ii) The graph G(R) is a block graph with #R blocks if and only if R is strongly compatible.

Place, publisher, year, edition, pages
2002. Vol. 244, no 1-3, 153-166 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-13675DOI: 10.1016/S0012-365X(01)00080-2ISI: 000173839800015Scopus ID: 2-s2.0-31244433852OAI: oai:DiVA.org:miun-13675DiVA: diva2:412187
Conference
4th Slovenian Graph Theory Conference BLED, SLOVENIA, JUN 28-JUL 02, 1999
Note

4th Slovenian Graph Theory Conference, Jun 28-Jul 02, 1999, Bled, Slovenia

Available from: 2011-04-21 Created: 2011-04-21 Last updated: 2016-09-27Bibliographically approved

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  • asciidoc
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