摘要
Let k and h be two integers, 0≤h<k. Let G be a connected graph with minimum degree at least k. The conditional h-edge-connectivity of G, denoted by λ(h) (G), is defined as the minimum cardinality |S| of a set S of edges in G such that G-S is disconnected and is of minimum degree at least h. This type of edge-connectivity is a generalization of the traditional edge-connectivity and can more accurately measure the fault-tolerance of networks. In this paper, we will first show thatλ A(2)(G)≤g(k-2) for a k(≥3)-regular graph G provided G is neither K4 and K5 nor K3,a, where g is the length of a shortest cycle of G, then show that λ(h)(Qk)=(k-h)2h for a k-dimensional cube Qk.
Let k and h be two integers, 0≤h<k. Let G be a connected graph with minimum degree at least k. The conditional h-edge-connectivity of G, denoted by λ(h) (G), is defined as the minimum cardinality |S| of a set S of edges in G such that G-S is disconnected and is of minimum degree at least h. This type of edge-connectivity is a generalization of the traditional edge-connectivity and can more accurately measure the fault-tolerance of networks. In this paper, we will first show thatλ A(2)(G)≤g(k-2) for a k(≥3)-regular graph G provided G is neither K4 and K5 nor K3,a, where g is the length of a shortest cycle of G, then show that λ(h)(Qk)=(k-h)2h for a k-dimensional cube Qk.
基金
the National Natural Science Foundation of China (No.19971086).
