Abstract

This paper presents a comprehensive study of cubic vertex-transitive graphs with an order of up to 1280 vertices. Additionally, tetravalent arc-transitive graphs with an order of up to 640 vertices are also determined. The investigation combines novel theoretical insights with rigorous computer calculations to identify and classify these graph structures. The results contribute to a deeper understanding of the properties and patterns exhibited by cubic vertex-transitive graphs, offering valuable insights for further research in this field.

Key words: Cubic graphs; Vertex-transitive graphs; Tetravalent graphs; Combinatorics.