Edge disjoint paths have a closed relationship with edge connectivity and are anticipated to garner increased attention in the study of the reliability and edge fault tolerance of a readily scalable interconnection network. Note that this interconnection network is always modeled as a connected graph G. The minimum of some of modified edge-cuts of a connected graph G, also known as the h-extra edge-connectivity of a graph G (\(\lambda _{h}(G)\)), is defined as the maximum number of the edge disjoint paths connecting any two disjoint connected subgraphs with h vertices in the graph G. From the perspective of edge-cut, the smallest cardinality of a collection of edges, whose removal divides the whole network into several connected subnetworks having at least h vertices, is the h-extra edge-connectivity of the underlying topological architecture of an interconnection network G. This paper demonstrates that the h-extra edge-connectivity of the pentanary n-cube (\(\lambda _{h}(K_{5}^{n})\)) appears a concentration behavior for around 50 percent of \(h\le \lfloor 5^{n}/2\rfloor \) as n approaches infinity. Let \(e=1\) for n is even and \(e=0\) for n is odd. It mainly concentrates on the value \([4g(\lceil \frac{n}{2}\rceil -r)-g(g-1)]5^{\lfloor \frac{n}{2}\rfloor +r}\) for \(g5^{\lfloor \frac{n}{2}\rfloor +r}-\lfloor \frac{[(g-1)^{2}+1]5^{2r+e}}{3}\rfloor \le h\le g5^{\lfloor \frac{n}{2}\rfloor +r}\), where \(r=1, 2,\cdots , \lceil \frac{n}{2}\rceil -2\), \(g\in \{1, 2,3,4\}\); \(r=\lceil \frac{n}{2}\rceil -1\), \(g\in \{1,2\}\). Furthermore, it is shown that the above upper bound and lower bound of h are sharp.

边缘不相交路径与边缘连接性具有密切关系，预计在易于扩展的互连网络的可靠性和边缘容错性研究中会受到更多关注。请注意，该互连网络始终被建模为连通图G。连通图G的一些修改边割的最小值，也称为图G的h额外边连通性( \(\lambda _{h}(G)\) )，被定义为最大值连接图G中任意两个具有h 个顶点的不相交连通子图的边不相交路径的数量。从边割的角度来看，边集合的最小基数，其去除将整个网络划分为多个至少具有h 个顶点的连通子网络，即为互连网络底层拓扑结构的h额外边连通性G。本文证明，五元n立方体 ( \(\lambda _{h}(K_{5}^{n})\) )的h额外边连通性在 50% 左右出现集中行为(当n接近无穷大时，h\le \lfloor 5^{n}/2\rfloor \)。设\(e=1\)表示n为偶数，\(e=0\)表示n为奇数。主要集中在值\([4g(\lceil \frac{n}{2}\rceil -r)-g(g-1)]5^{\lfloor \frac{n}{2}\rfloor + r}\)为\(g5^{\lfloor \frac{n}{2}\rfloor +r}-\lfloor \frac{[(g-1)^{2}+1]5^{2r+e }}{3}\rfloor \le h\le g5^{\lfloor \frac{n}{2}\rfloor +r}\)，其中\(r=1, 2,\cdots , \lceil \frac{ n}{2}\rceil -2\) , \(g\in \{1, 2,3,4\}\) ; \(r=\lceil \frac{n}{2}\rceil -1\)、\(g\in \{1,2\}\)。进一步表明，上述h的上界和下界是尖锐的。