Abstract
Classical edge-connectivity is a vital metric to characterize fault tolerance and reliability of network-based multiprocessor system. As two generalizations of classical edge-connectivity, super edge-connectivity and average degree edge-connectivity are two important parameters to assess the fault tolerability of a multiprocessor system by imposing some constraints on the degree of survival graph. In this work, we focus on k-super edge connectivity λk(Qn3) and a-average degree edge connectivity λa¯(Qn3) of the 3-ary n-cube. We first show that λ2a¯(Qn3)=2(n−a)3a for 0≤a≤n−1, n≥1 and λ2a+1¯(Qn3)=2(2n−2a−1)3a for 0≤a≤n−2, n≥2. Moreover, we determine that λ2a(Qn3)=λ2a¯(Qn3), and λ2a+1(Qn3)=λ2a+1¯(Qn3), which indicates that these two kinds of metrics possess the same robustness in a 3-ary n-cube.
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