Description: An arc-transitive graph is a type of graph in which, for any pair of arcs, there exists an automorphism that can map one arc to the other. This means that the structure of the graph is highly symmetric, allowing the relationships between arcs to be interchangeable through transformations that preserve the graph’s structure. In more technical terms, an automorphism is a function that maps a graph to itself in such a way that the connections between nodes are maintained. This symmetry property in arc-transitive graphs makes them interesting for study in graph theory and combinatorics, as they allow for a deeper exploration of the structural properties of graphs. Arc-transitive graphs are a specific case of transitive graphs, where symmetry extends to arcs rather than just vertices. This characteristic makes them useful in various research areas, including group theory and combinatorial geometry, where the aim is to understand how structures can be transformed and analyzed through their inherent symmetries.
