Arc-connectivity And Super Arc-connectivity Of Strongly Connected Mixed Cayley Digraphs

The connectivity of a graph is an important parameter of the reliabilityof a graph, and the underlying topology of a network is often modeled as agraph. So, some classical notations of graph theory, such as the connectivityand the edge(arc)-connectivity, is utilized to measure the reliability of net-works. For further study, many variations have been introduced, which areknown as higher connectedness, such as super-connectivity, super-edge(arc)connectivity, restricted edge connectivity, super-restricted edge connectednessetc.Let G be a finite group, S₀, S₁(?)G \ {1G}, T₀, T₁ (?)G. Define the mixedCayley digraph X = MD(G,S₀,S₁,T₀,T₁): vertex set is G×{0,1}; arc setis {((g,i),(s_j·g,i)),((g,0),(t0·g,1)),((t₁·g,1), (g,0))| g∈G,s_j∈S_j,t₀∈T₀,t₁∈T₁}, for i = 0,1. This definition is defined by professor J.X. Meng, wemainly study arc connectedness and super-arc connectedness of the stronglyconnected mixed Cayley digraphs in this paper.In Chapter 1, we introduce the background of our study and some nota-tions, and then discuss the basic properties of strongly connected mixed Cayleydigraphs. In Chapter 2, we study the arc connectedness of strongly connectedmixed Cayley digraphs. In Chapter 3, we study the super-arc connectednessof strongly connected mixed Cayley digraphs. The main result of this paperis that for all but a few exceptions, strongly connected mixed Cayley digraphsare maximally arc-connected and super arc-connected.