Matches in SemOpenAlex for { <https://semopenalex.org/work/W3035018239> ?p ?o ?g. }
Showing items 1 to 59 of
59
with 100 items per page.
- W3035018239 abstract "We shall consider problems in two broad areas of mathematics, namely the area of the degree diameter problem and the area of regular maps. In the degree diameter problem we investigate finding graphs as large as possible with a given degree and diameter. Further, we may consider additional properties of such extremal graphs, for example restrictions on the kinds of symmetries that the graph in question exhibits. We provide two pieces of research relating to the degree diameter problem. First, we provide a new derivation of the Hoffman-Singleton graph and show that this derivation may be used with minor modification to derive the Bosak graph. Ultimately we show that no further natural modification of the construction we use can derive any other Moore or mixed-Moore graphs. Second, we answer the previously open question of whether the Gomez graphs, which are known to be vertex-transitive, are in addition also Cayley. In doing this, we also generalise the construction of the Gomez graphs and show that the Gomez graphs are the largest graphs for given degree and diameter following the generalised construction. We also provide two pieces of research relating to regular maps. We aim to address the related questions of for which triples of parameters k, l and m there exist finite regular maps of face length k, vertex order l and Petrie walk length m. We then address the related question of determining for which n there exist regular maps which are self dual and self Petrie dual which have face length, vertex order and Petrie dual walk length n. We address both questions by constructions of regular maps in fractional linear groups, necessarily leading us to study some interesting related number theoretic questions." @default.
- W3035018239 created "2020-06-19" @default.
- W3035018239 creator A5033331641 @default.
- W3035018239 date "2020-05-04" @default.
- W3035018239 modified "2023-09-24" @default.
- W3035018239 title "Extremal Metric and Topological Properties of Vertex Transitive and Cayley Graphs" @default.
- W3035018239 hasPublicationYear "2020" @default.
- W3035018239 type Work @default.
- W3035018239 sameAs 3035018239 @default.
- W3035018239 citedByCount "0" @default.
- W3035018239 crossrefType "dissertation" @default.
- W3035018239 hasAuthorship W3035018239A5033331641 @default.
- W3035018239 hasConcept C114614502 @default.
- W3035018239 hasConcept C118615104 @default.
- W3035018239 hasConcept C120204988 @default.
- W3035018239 hasConcept C121332964 @default.
- W3035018239 hasConcept C132525143 @default.
- W3035018239 hasConcept C160446614 @default.
- W3035018239 hasConcept C24890656 @default.
- W3035018239 hasConcept C2775997480 @default.
- W3035018239 hasConcept C33923547 @default.
- W3035018239 hasConcept C80899671 @default.
- W3035018239 hasConceptScore W3035018239C114614502 @default.
- W3035018239 hasConceptScore W3035018239C118615104 @default.
- W3035018239 hasConceptScore W3035018239C120204988 @default.
- W3035018239 hasConceptScore W3035018239C121332964 @default.
- W3035018239 hasConceptScore W3035018239C132525143 @default.
- W3035018239 hasConceptScore W3035018239C160446614 @default.
- W3035018239 hasConceptScore W3035018239C24890656 @default.
- W3035018239 hasConceptScore W3035018239C2775997480 @default.
- W3035018239 hasConceptScore W3035018239C33923547 @default.
- W3035018239 hasConceptScore W3035018239C80899671 @default.
- W3035018239 hasLocation W30350182391 @default.
- W3035018239 hasOpenAccess W3035018239 @default.
- W3035018239 hasPrimaryLocation W30350182391 @default.
- W3035018239 hasRelatedWork W126284025 @default.
- W3035018239 hasRelatedWork W2009466635 @default.
- W3035018239 hasRelatedWork W2167900279 @default.
- W3035018239 hasRelatedWork W2252330517 @default.
- W3035018239 hasRelatedWork W2295733696 @default.
- W3035018239 hasRelatedWork W2296666114 @default.
- W3035018239 hasRelatedWork W2545735748 @default.
- W3035018239 hasRelatedWork W2605191020 @default.
- W3035018239 hasRelatedWork W2624585283 @default.
- W3035018239 hasRelatedWork W2758407290 @default.
- W3035018239 hasRelatedWork W2764159756 @default.
- W3035018239 hasRelatedWork W2904246893 @default.
- W3035018239 hasRelatedWork W2962916098 @default.
- W3035018239 hasRelatedWork W3010302700 @default.
- W3035018239 hasRelatedWork W3011227702 @default.
- W3035018239 hasRelatedWork W3034671197 @default.
- W3035018239 hasRelatedWork W3098159482 @default.
- W3035018239 hasRelatedWork W3110915506 @default.
- W3035018239 hasRelatedWork W2764108817 @default.
- W3035018239 hasRelatedWork W2766085142 @default.
- W3035018239 isParatext "false" @default.
- W3035018239 isRetracted "false" @default.
- W3035018239 magId "3035018239" @default.
- W3035018239 workType "dissertation" @default.