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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/12318

Title: The group structure of pivot and loop complementation on graphs and set systems
Authors: Brijder, Robert
Hoogeboom, Hendrik Jan
Issue Date: 2011
Citation: EUROPEAN JOURNAL OF COMBINATORICS, 32(8). p. 1353-1367
Abstract: We study the interplay between the principal pivot transform (pivot) and loop complementation for graphs. This is done by generalizing loop complementation (in addition to pivot) to set systems. We show that the operations together, when restricted to single vertices, form the permutation group S(3). This leads, e.g., to a normal form for sequences of pivots and loop complementation on graphs. The results have consequences for the operations of local complementation and edge complementation on simple graphs: an alternative proof of a classic result involving local and edge complementation is obtained, and the effect of sequences of local complementations on simple graphs is characterized. (C) 2011 Elsevier Ltd. All rights reserved.
Notes: [Brijder, R] Hasselt Univ, Diepenbeek, Belgium. [Brijder, R] Transnat Univ Limburg, Limburg, Belgium. [Hoogeboom, HJ] Leiden Univ, Leiden Inst Adv Comp Sci, NL-2300 RA Leiden, Netherlands. robert.brijder@uhasselt.be
URI: http://hdl.handle.net/1942/12318
DOI: 10.1016/j.ejc.2011.03.002
ISI #: 000295436000017
ISSN: 0195-6698
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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