Upper bound of the third edge-connectivity of graphs

<正>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.