A3 Refereed book chapter or chapter in a compilation book
On Involutions Arising from Graphs
Authors: Hage J, Harju T
Editors: Condon Anne, Harel David, Kok Joost N., Salomaa Arto, Winfree Erik
Publication year: 2009
Journal: Algorithmic bioprocesses
Book title : Algorithmic Bioprocesses
Journal name in source: ALGORITHMIC BIOPROCESSES
Journal acronym: NAT COMP SER
Series title: Natural Computing Series
First page : 623
Last page: 630
Number of pages: 8
ISBN: 978-3-540-88868-0
ISSN: 1619-7127
DOI: https://doi.org/10.1007/978-3-540-88869-7_30
Abstract
We investigate various aspects of involutions of groups, i.e. anti-automorphisms of order at most two. The emphasis is on finite Abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated Abelian groups with identity as the involution. The present paper is motivated by our research into switching classes of combinatorial graphs where the edges have skew gains.
We investigate various aspects of involutions of groups, i.e. anti-automorphisms of order at most two. The emphasis is on finite Abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated Abelian groups with identity as the involution. The present paper is motivated by our research into switching classes of combinatorial graphs where the edges have skew gains.
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