On the Baer–Lovász–Tutte construction of groups from graphs: Isomorphism types and homomorphism notions

He, X; Qiao, Y

On the Baer–Lovász–Tutte construction of groups from graphs: Isomorphism types and homomorphism notions

He, X Qiao, Y

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: European Journal of Combinatorics, 2021, 98, pp. 103404
Issue Date:: 2021-12-01

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Field	Value	Language
dc.contributor.author	He, X
dc.contributor.author	Qiao, Y https://orcid.org/0000-0003-4334-1449
dc.date.accessioned	2022-01-28T00:03:53Z
dc.date.available	2022-01-28T00:03:53Z
dc.date.issued	2021-12-01
dc.identifier.citation	European Journal of Combinatorics, 2021, 98, pp. 103404
dc.identifier.issn	0195-6698
dc.identifier.uri	http://hdl.handle.net/10453/153691
dc.description.abstract	Let p be an odd prime. From a simple undirected graph G, through the classical procedures of Baer (1938), Tutte (1947) and Lovász (1989), there is a p-group PG of class 2 and exponent p that is naturally associated with G. Our first result is to show that this construction of groups from graphs respects isomorphism types. That is, given two graphs G and H, G and H are isomorphic as graphs if and only if PG and PH are isomorphic as groups. Our second contribution is a new homomorphism notion for graphs. Based on this notion, a category of graphs can be defined, and the Baer–Lovász–Tutte construction naturally leads to a functor from this category of graphs to the category of groups.
dc.language	en
dc.publisher	Elsevier BV
dc.relation	http://purl.org/au-research/grants/arc/DP200100950
dc.relation.ispartof	European Journal of Combinatorics
dc.relation.isbasedon	10.1016/j.ejc.2021.103404
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics
dc.subject.classification	Computation Theory & Mathematics
dc.title	On the Baer–Lovász–Tutte construction of groups from graphs: Isomorphism types and homomorphism notions
dc.type	Journal Article
utslib.citation.volume	98
utslib.for	0101 Pure Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	closed_access	*
dc.date.updated	2022-01-28T00:03:51Z
pubs.publication-status	Published
pubs.volume	98

Abstract:

Let p be an odd prime. From a simple undirected graph G, through the classical procedures of Baer (1938), Tutte (1947) and Lovász (1989), there is a p-group PG of class 2 and exponent p that is naturally associated with G. Our first result is to show that this construction of groups from graphs respects isomorphism types. That is, given two graphs G and H, G and H are isomorphic as graphs if and only if PG and PH are isomorphic as groups. Our second contribution is a new homomorphism notion for graphs. Based on this notion, a category of graphs can be defined, and the Baer–Lovász–Tutte construction naturally leads to a functor from this category of graphs to the category of groups.

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http://hdl.handle.net/10453/153691