相关论文: On conditional fault tolerance of hierarchical cub…
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,…
Fault tolerance of an $(n,k)$-star network is measured by its $h$-super connectivity $\kappa_s^{(h)}$ or $h$-super edge-connectivity $\lambda_s^{(h)}$. Li {\it et al.} [Appl. Math. Comput. 248 (2014), 525-530; Math. Sci. Lett. 1 (2012),…
Faulty networks are useful because link or node faults can occur in a network. This paper examines the Hamiltonian properties of hypercubes under certain conditional faulty edges. Let consider the hypercube \( Q_n \), for \( n \geq 5 \) and…
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…
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…
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…
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…
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…
The restricted $h$-connectivity of a graph $G$, denoted by $\kappa^h(G)$, is defined as the minimum cardinality of a set of vertices $F$ in $G$, if exists, whose removal disconnects $G$ and the minimum degree of each component of $G-F$ is…
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…
As a generalization of the traditional connectivity, the g-component edge connectivity c{\lambda}g(G) of a non-complete graph G is the minimum number of edges to be deleted from the graph G such that the resulting graph has at least g…
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…
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…
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…
Twisted hypercube-like networks (THLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, M\"obius cubes, twisted cubes and…
Let $G=(V, E)$ be a connected graph, a subset $S\subseteq V(G)$ is called an $R^{g}$-vertex-cut of $G$ if $G-F$ is disconnected and any vertex in $G-F$ has at least $g$ neighbours in $G-F$. The $R^{g}$-vertex-connectivity is the size of the…
The augmented cube $AQ_n$, proposed by Choudum and Sunitha [S. A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a $(2n-1)$-regular $(2n-1)$-connected graph $(n\ge 4)$. This paper determines that the 2-extra…
Structure connectivity and substructure connectivity are innovative indicators for assessing network reliability and fault tolerance. Similarly, fault diameter evaluates fault tolerance and transmission delays in networks. This paper…