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DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Knauer, Kolja | - |
dc.contributor.author | Vidal i Garcia, Ernest | - |
dc.date.accessioned | 2023-11-15T08:13:43Z | - |
dc.date.available | 2023-11-15T08:13:43Z | - |
dc.date.issued | 2023-06-13 | - |
dc.identifier.uri | http://hdl.handle.net/2445/203648 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Kolja Knauer | ca |
dc.description.abstract | [en] First, a wide definition of Cayley graphs is presented. We focus on the notion of monoid graph: a graph is a monoid graph if it is isomorphic to the underlying graph of the Cayley graph $\operatorname{Cay}(M, C)$ of some monoid $M$ with some connection set $C \subseteq M$. Secondly, the family of Generalized Petersen Graphs $G(n, k)$ is presented. We study the open question whether every Generalized Petersen Graph is a monoid graph, and we focus on the smallest one for which the question remains unanswered: $G(7,2)$. Finally, we explore the feasibility of using the computer to search for a possible monoid for $G(7,2)$. We conclude that it is not viable to check all the possibilities with the proposed algorithms. Nevertheless, we are able to provide a computer-assisted proof that if $G(7,2)$ is a monoid graph then the connection set $C$ does not have any invertible element. | ca |
dc.format.extent | 49 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Ernest Vidal i Garcia, 2023 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Teoria de grafs | ca |
dc.subject.classification | Monoides | - |
dc.subject.classification | Semigrups | ca |
dc.subject.classification | Teoria de grups | ca |
dc.subject.classification | Treballs de fi de grau | ca |
dc.subject.other | Graph theory | en |
dc.subject.other | Monoids | - |
dc.subject.other | Semigroups | en |
dc.subject.other | Group theory | en |
dc.subject.other | Bachelor's theses | en |
dc.title | Monoid graphs and generalized Petersen graphs | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_vidal_i_garcia_ernest.pdf | Memòria | 613.81 kB | Adobe PDF | View/Open |
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