In a communication network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a connected graph as model-ing a network, the rupture degree of a graph is one measure of graph vulnerability and it is defined by γ{G) = max{ω(G - S) - ∣S∣ - m(G - S) : S C V(G),ω{G - S) > 1}, where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. In this paper, general results on the rupture degree of a graph are considered. Firstly, some bounds on the rupture degree are given. Further, rupture degree of a complete κ-ary tree is calculated. Also several results are given about complete κ-ary tree and graph operations. Finally, we give formulas for the rupture degree of the cartesian product of some special graphs.
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机译：在通信网络中，漏洞衡量的是在某些站点或通信链路发生故障后网络对操作中断的抵抗力。如果我们认为连通图是对网络进行建模，则图的破裂程度是图易损性的一种度量，它由γ{G）= max {ω（G（S）-∣S∣-m （G-S）：SCV（G），ω{G-S）> 1}，其中w（GS-S）是G-S的分量数，而m（GS-S）是最大数的阶数在本文中，考虑了关于图的破裂度的一般结果。首先，给出了断裂程度的一些界限。此外，计算完整的κ元树的破裂度。还给出了有关完整κ元树和图操作的一些结果。最后，我们给出了一些特殊图的笛卡尔积破裂程度的公式。
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