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Title: | The group structure of pivot and loop complementation on graphs and set systems | Authors: | BRIJDER, Robert Hoogeboom, Hendrik Jan |
Issue Date: | 2011 | Publisher: | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD | Source: | 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 | Document URI: | http://hdl.handle.net/1942/12318 | ISSN: | 0195-6698 | e-ISSN: | 1095-9971 | DOI: | 10.1016/j.ejc.2011.03.002 | ISI #: | 000295436000017 | Rights: | Copyright © 2011 Elsevier Ltd. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2012 |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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pivots_permutations.pdf | Peer-reviewed author version | 233.9 kB | Adobe PDF | View/Open |
brijder 1.pdf Restricted Access | Published version | 390.79 kB | Adobe PDF | View/Open Request a copy |
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