Super Arc-connected Regular Digraphs With Two Orbits

The connectivity is one of the important parameter of graphs. The underlying to pology of a network is often modedled as a graph. The concept of connectivity in graph theory is an important measure for the networks. With the passage of time and research progress of science the research of connectivity in depth. People have been satis?ed with the ?rst(edge) connectivity. For further study, many variations have been introduced,which are known as higher connectedness, such as super- λ( super- κ), restricted edge connectivity and super-restricted edge connectedness etc, also done a lot of research and have a lot of research. However, the study of transitive graphs(one orbit) and edge transitive graphs(one edge orbit) have a lot of research. We consider relatively weaker case than transitive graphs: graphs with two orbits.We call the set {vg: g ∈ Aut(G)} an orbit of Aut(D), if v ∈ V(G). A graph is called double- orbit graph if it contains exactly two orbits. In this paper, we mainly study the super arc-connected regular digraphs with two orbits.In Chapter 1, we introduce the background of our study and some notations, and recall known results on various kinds of edge connectivity. In Chapter 2, we ?rst study the λ-superatoms then study the super arc-connected regular digraphs with two orbits.We prove that a k-regular(k ≥ 3) strongly connected digraph with two orbits and g(D) ≥k + 1, then D is super-λ.