摘要
Let G be a simple connected graph of order n ≥ 6. The third edge-connectivity of G is defined as the minimum cardinality over all the sets of edges, if any, whose deletion disconnects G and every component of the resulting graph has at least 3 vertices. In this paper, we first characterize those graphs whose third-edge connectivity is well defined,then establish the tight upper bound for the third edge-connectivity.
Let G be a simple connected graph of order n≥6. The third edge-connectivity of G is defined as the minimum cardinality over all the sets of edges, if any, whose deletion disconnects G and every component of the resulting graph has at least 3 vertices. In this paper, we first characterize those graphs whose third-edge connectivity is well defined, then establish the tight upper bound for the third edge-connectivity.
基金
This work was supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.102055)
the Natural Science Foundation of Zhejiang Normal University
The second author was supported by the National Natural Science Foundation of China(Grant No.19971056).
