Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/203648
Title: | Monoid graphs and generalized Petersen graphs |
Author: | Vidal i Garcia, Ernest |
Director/Tutor: | Knauer, Kolja |
Keywords: | Teoria de grafs Monoides Semigrups Teoria de grups Treballs de fi de grau Graph theory Monoids Semigroups Group theory Bachelor's theses |
Issue Date: | 13-Jun-2023 |
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. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Kolja Knauer |
URI: | http://hdl.handle.net/2445/203648 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
tfg_vidal_i_garcia_ernest.pdf | Memòria | 613.81 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License