Edge-connectivity of regular graphs with two orbits
Let \(G=(V,E)\) be a simple connected graph and \(x\in V(G)\). The set \(\{x^g : g\in Aut(G)\}\) is called an orbit of \(Aut(G)\), the automorphism group of \(G\). This paper determines the edge-connectivity of \(3\)-regular and \(4\)-regular connected graphs with two orbits, and proves the existence of \(k\)-regular \(m\)-edge-connected graphs with two orbits for some given integers \(k\) and \(m\). Furthermore, it is proved that the edge-connectivity of a \(k\)-regular connected graph with two orbits and girth at least \(5\) attains its regular degree \(k\).
scientific article; zbMATH DE number 5300689