相关论文: Generalized Measures of Fault Tolerance in (n,k)-s…
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…
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),…
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…
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,…
This paper shows that, for any integers $n$ and $k$ with $0\leqslant k \leqslant n-2$, at least $(k+1)!(n-k-1)$ vertices or edges have to be removed from an $n$-dimensional star graph to make it disconnected and no vertices of degree less…
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…
Vertex-fault-tolerance was introduced by Hayes~\cite{Hayes1976} in 1976, and since then it has been systematically studied in different aspects. In this paper we study $k$-vertex-fault-tolerant graphs for $p$ disjoint complete graphs of…
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…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a natural generalization of the concept of connectivity $\kappa(G)$, which is just for $k=2$. Total graph is generalized line graph and a large…
For $S\subseteq V(G)$ with $|S|\ge 2$, let $\kappa_G (S)$ denote the maximum number of internally disjoint trees connecting $S$ in $G$. For $2\le k\le n$, the generalized $k$-connectivity $\kappa_k(G)$ of an $n$-vertex connected graph $G$…
The concept of generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ was introduced by Chartrand et al. in recent years. In our early paper, extremal theory for this graph parameter was started. We determined the minimal number of…
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 generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984. It is natural to introduce the concept of generalized $k$-edge-connectivity $\lambda_k(G)$. For general $k$, the generalized…
Recent work has established that, for every positive integer $k$, every $n$-node graph has a $(2k-1)$-spanner on $O(f^{1-1/k} n^{1+1/k})$ edges that is resilient to $f$ edge or vertex faults. For vertex faults, this bound is tight. However,…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized…
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical"$ $ graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works…
We give some existence/nonexistence statements on universal graphs, which under GCH give a necessary and sufficient condition for the existence of a universal graph of size lambda with no K(kappa), namely, if either kappa is finite or…
Given nonnegative integers, $s$ and $k$, an $(s,k)$-polar partition of a graph $G$ is a partition $(A,B)$ of $V_G$ such that $G[A]$ and $\overline{G[B]}$ are complete multipartite graphs with at most $s$ and $k$ parts, respectively. If $s$…
Given a graph $Y$ on $n$ vertices and a desired level of fault-tolerance $k$, an objective in fault-tolerant system design is to construct a supergraph $X$ on $n + k$ vertices such that the removal of any $k$ nodes from $X$ leaves a graph…