3-extra connectivity of 3-ary n-cube networks

Neighbor connectivity of $k$-ary $n$-cubes

The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an interconnection network, this means that the failure of a network node causes failures of all its neighbors. We completely determine the neighbor connectivity of $k$-ary $n$-cubes for all $n\ge1$ and $k\ge2$.

Strong Menger connectedness of augmented $k$-ary $n$-cubes

A connected graph $G$ is called strongly Menger (edge) connected if for any two distinct vertices $x,y$ of $G$, there are $\min \{{\rm deg}_G(x), {\rm deg}_G(y)\}$ vertex(edge)-disjoint paths between $x$ and $y$. In this paper, we consider strong Menger (edge) connectedness of the augmented $k$-ary $n$-cube $AQ_{n,k}$, which is a variant of $k$-ary $n$-cube $Q_n^k$. By exploring the topological proprieties of $AQ_{n,k}$, we show that $AQ_{n,3}$ for $n\geq 4$ (resp.\ $AQ_{n,k}$ for $n\geq 2$ and $k\geq 4$) is still strongly Menger connected even when there are $4n-9$ (resp.\ $4n-8$) faulty vert…

Extra connectivity measures of 3-ary n-cubes

The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The k-ary n-cube is an important interconnection network of parallel computing systems. The 1-restricted connectivity of k-ary n-cubes has been obtained by Chen et al. for k > 3 in [Y.-C. Chen, J. J. M. Tan, Restricted connectivity for three families of interconnection networks, Applied Mathematics and Computation 188 (2) (2007)1848--1855]. Nevertheless, the h-extra connectivity of 3-ary n-cubes has not been obtained yet. In this paper we prove that the 1…

On 3-extra connectivity of k-ary n-cubes

Given a graph G, a non-negative integer h and a set of vertices S, the h-extra connectivity of G is the cardinality of a minimum set S such that G-S is disconnected and each component of G-S has at least h+1 vertices. The 2-extra connectivity of k-ary n-cube is gotten by Hsieh et al. in [Theoretical Computer Science, 443 (2012) 63-69]. In this paper, we obtained the h-extra connectivity of the k-ary n-cube networks for h=3.

嵌入特定圆柱和树中的3_ary n立方体的精确线长

Exact Wirelength of Embedding 3-Ary n-Cubes into certain Cylinders and Trees

研究了将3_ary n立方体嵌入特定圆柱和树中的线长问题，提出计算方法并分析其在并行系统中的应用价值。

A novel view: edge isoperimetric methods and reliability evaluation of several kinds of conditional edge-connectivity of interconnection networks

Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different $\mathcal{P}$-conditional edge-connectivity. With the help of edge isoperimetric problem's method in combinatorics, this paper mainly offers a novel and unified view to investigate the $\mathcal{P}$-conditional edge-connectivities of hamming graph $K_{L}^{n}$ with satisfying the property that each minimum $\mathcal{P}$-conditional edge-cut separates the $K_{L}^{n}$ just into two components, such as …