Related papers: Reliability evaluation of folded hypercubes in ter…

The $g$-component edge connectivity $c\lambda_g(G)$ of a non-complete graph $G$ is the minimum number of edges whose deletion results in a graph with at least $g$ components. In this paper, we determine the component edge connectivity of…

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…

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…

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 processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly…

Let $ H $ be a connected subgraph of a graph $ G $. The structure connectivity of $ G $, denoted by $ \kappa(G;H) $, is the minimum number of a set of connected subgraphs in $ G $, whose removal disconnects $ G $ and each element in the set…

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 $F$…

The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…

Connectivity and diagnosability are important parameters in measuring the fault tolerance and reliability of interconnection networks. The $R^g$-vertex-connectivity of a connected graph $G$ is the minimum cardinality of a faulty set…

For an integer $\ell\geqslant 2$, the $\ell$-component connectivity of a graph $G$, denoted by $\kappa_{\ell}(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a…

Let $G$ be a graph and $T$ a certain connected subgraph of $G$. The $T$-structure connectivity $\kappa(G; T)$ (or resp., $T$-substructure connectivity $\kappa^{s}(G; T)$) of $G$ is the minimum number of a set of subgraphs…

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…

Given a connected graph $G$ and a non-negative integer $g$, the {\em $g$-extra connectivity} $\k_g(G)$ of $G$ is the minimum cardinality of a set of vertices in $G$, if it exists, whose deletion disconnects $G$ and leaves each remaining…

The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is a generalization of the traditional connectivity. It is well known that the generalized $k$-connectivity is an important indicator for measuring the fault…

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…

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 $\ell$-component connectivity (or $\ell$-connectivity for short) of a graph $G$, denoted by $\kappa_\ell(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a…

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…

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…

Let $S\subseteq V(G)$ and $\kappa_{G}(S)$ denote the maximum number $k$ of edge-disjoint trees $T_{1}, T_{2}, \cdots, T_{k}$ in $G$ such that $V(T_{i})\bigcap V(T_{j})=S$ for any $i, j \in \{1, 2, \cdots, k\}$ and $i\neq j$. For an integer…