关键词: 点可迁图, 边连通度, 限制

Abstract:

A 3restricted edge cut is an edge cut of a connected graph which separates this graph into components each having order at least 3. The minimum size of 3\|restricted edge cuts of graph G is called its 3restricted edge c onnectivity λ_3(G),which is bounded above by the minimum cardinality ξ_3(G)of the coboundary of its connected vertex\|induced subgraph of orde r 3. A graph G is called maximal 3 restricted edge connected if λ_3(G)= ξ_3(G). It is known that networks with greater 3 restricted  edge connectivity is more reliable in certain sense. The author proves in this paper that a conected k regular vertex transitive graph is maximal 3 restricted edge connected if it has girth at least 5.

Key words: Vertex transitive graph, Edge connectivity, Restricted