Related papers: On fault tolerance of (n,k)-star networks
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\leqslant k \leqslant n-1$ and $0\leqslant h \leqslant n-k$, and determines…
This paper considers a kind of generalized measure $\kappa_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ and determines $\kappa_s^{(h)}(S_{n,k})=n+h(k-2)-1$ for $2 \leqslant k \leqslant n-1$ and $0\leqslant h \leqslant…
This paper considers the conditional fault tolerance, $h$-super connectivity $\kappa^{h}$ and $h$-super edge-connectivity $\lambda^{h}$ of the hierarchical cubic network $HCN_n$, an attractive alternative network to the hypercube, and shows…
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in a hypercube-like graph $G_n$ which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes,…
The edge-fault-tolerance of networks is of great significance to the design and maintenance of networks. For any pair of vertices $u$ and $v$ of the connected graph $G$, if they are connected by $\min \{ \deg_G(u),\deg_G(v)\}$ edge-disjoint…
Last decade, numerous giant data center networks are built to provide increasingly fashionable web applications. For two integers $m\geq 0$ and $n\geq 2$, the $m$-dimensional DCell network with $n$-port switches $D_{m,n}$ and…
The exchanged hypercube $EH(s,t)$, proposed by Loh {\it et al.} [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube $Q_{s+t+1}$. This paper…
The connectivity is an important parameter to evaluate the robustness of a network. As a generalization, structure connectivity and substructure connectivity of graphs were proposed. For connected graphs $G$ and $H$, the $H$-structure…
Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. $k$-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks. Matching preclusion and…
As the scale of data centers continues to grow, there is an increasing demand for interconnection networks to resist malicious attacks. Hence, it is necessary to evaluate the reliability of networks under various fault patterns. The family…
The connectivity of a network directly signifies its reliability and fault-tolerance. Structure and substructure connectivity are two novel generalizations of the connectivity. Let $H$ be a subgraph of a connected graph $G$. The structure…
Hypercube is one of the most important networks to interconnect processors in multiprocessor computer systems. Different kinds of connectivities are important parameters to measure the fault tolerability of networks. Lin et…
The generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ is a parameter that can measure the reliability of a network $G$ to connect any $k$ vertices in $G$, which is proved to be NP-complete for a general graph $G$. Let $S\subseteq…
As a generalization of vertex connectivity, for connected graphs $G$ and $T$, the $T$-structure connectivity $\kappa(G, T)$ (resp. $T$-substructure connectivity $\kappa^{s}(G, T)$) of $G$ is the minimum cardinality of a set of subgraphs $F$…
Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\leq…
Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The $(n, k)$-enhanced hypercube $Q_{n,k}$, as a variation of the hypercube $Q_{n}$, was proposed by Tzeng and Wei in…
A $k$-fault-tolerant connectivity preserver of a directed $n$-vertex graph $G$ is a subgraph $H$ such that, for any edge set $F \subseteq E(G)$ of size $|F| \le k$, the strongly connected components of $G - F$ and $H - F$ are the same.…
With graphs considered as natural models for many network design problems, edge connectivity $\kappa'(G)$ and maximum number of edge-disjoint spanning trees $\tau(G)$ of a graph $G$ have been used as measures for reliability and strength in…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
Let G be a connected graph and S be a set of vertices. 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 h-extra connectivity is an…