Bayi Road, Xining, Qinghai 810000, P. R. China. Received 30 May 2016. Accepted 8 March 2017. Communicated by Kai Salomaa. The edge rupture degree of a graph G, as one of measurement parameter of network vulnerability, is defined as Er(G) = max{ω(G − S) − |S| − m(G − S) : S ⊆ E(G), ω(G −.
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