scholarly journals Edge fault tolerance of graphs with respect to super edge connectivity

2012 ◽  
Vol 160 (4-5) ◽  
pp. 579-587 ◽  
Author(s):  
Yanmei Hong ◽  
Jixiang Meng ◽  
Zhao Zhang
Keyword(s):  
Fault Tolerance ◽  
Edge Connectivity ◽  
Edge Fault Tolerance

Reliability Evaluation of Augmented Cubes on Degree

2021 ◽  
Author(s):  
Mingzu Zhang ◽  
Xiaoli Yang ◽  
Xiaomin He ◽  
Zhuangyan Qin ◽  
Yongling Ma
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Minimum Degree ◽  
Tolerance Analysis ◽  
Reliability Evaluation ◽  
Affirmative Answer ◽  
Edge Connectivity ◽  
Minimum Number ◽  
Edge Fault Tolerance ◽  
Augmented Cube

The [Formula: see text]-dimensional augmented cube [Formula: see text], proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the [Formula: see text]-conditional edge-connectivity of a connected graph [Formula: see text], [Formula: see text], is defined as the minimum number of the cardinality of the edge-cut of [Formula: see text], if exists, whose removal disconnects this graph and keeps each component of [Formula: see text] having minimum degree at least [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] be three integers, where [Formula: see text], if [Formula: see text] and [Formula: see text], if [Formula: see text]. In this paper, we determine the exact value of the [Formula: see text]-conditional edge-connectivity of [Formula: see text], [Formula: see text] for each positive integer [Formula: see text] and [Formula: see text], and give an affirmative answer to Shinde and Borse’s corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139].

On Edge-Fault Tolerance in Augmented Cubes

2020 ◽  
Vol 20 (04) ◽  
pp. 2050013
Author(s):  
AMRUTA SHINDE ◽  
Y. M. BORSE
Keyword(s):  
Fault Tolerance ◽  
Upper Bound ◽  
Edge Connectivity ◽  
Edge Fault Tolerance ◽  
Augmented Cube

The augmented cube AQn is one of the important variations of the hypercube Qn. In this paper, we prove that the conditional h-edge connectivity of AQn with n ≥ 3 is 8n − 16 for h = 3 and 2n for h = 2n − 3. We also obtain an upper bound on the conditional h-edge connectivity for odd integer h satisfying [Formula: see text].

Component Edge Connectivity of Hypercubes

2018 ◽  
Vol 29 (06) ◽  
pp. 995-1001 ◽  
Author(s):  
Shuli Zhao ◽  
Weihua Yang ◽  
Shurong Zhang ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Complete Graph ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Optimal Solutions ◽  
Edge Connectivity ◽  
Important Measure ◽  
Minimum Number ◽  
Text Component

Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The [Formula: see text]-component edge connectivity [Formula: see text] of a non-complete graph [Formula: see text] is the minimum number of edges whose deletion results in a graph with at least [Formula: see text] components. Let [Formula: see text] be an integer and [Formula: see text] be the decomposition of [Formula: see text] such that [Formula: see text] and [Formula: see text] for [Formula: see text]. In this note, we determine the [Formula: see text]-component edge connectivity of the hypercube [Formula: see text], [Formula: see text] for [Formula: see text]. Moreover, we classify the corresponding optimal solutions.

Note on Applications of Linearly Many Faults

2019 ◽  
Vol 63 (9) ◽  
pp. 1406-1416 ◽  
Author(s):  
Mei-Mei Gu ◽  
Rong-Xia Hao ◽  
Eddie Cheng
Keyword(s):  
Fault Tolerance ◽  
General Property ◽  
Cayley Graphs ◽  
Connected Component ◽  
Edge Connectivity ◽  
Network Parameters ◽  
Large Connected Component

Abstract Most graphs have this property: after removing a linear number of vertices from a graph, the surviving graph is either connected or consists of a large connected component and small components containing a small number of vertices. This property can be applied to derive fault-tolerance related network parameters: extra edge connectivity and component edge connectivity. Using this general property, we obtained the $h$-extra edge connectivity and $(h+2)$-component edge connectivity of augmented cubes, Cayley graphs generated by transposition trees, complete cubic networks (including hierarchical cubic networks), generalized exchanged hypercubes (including exchanged hypercubes) and dual-cube-like graphs (including dual cubes).

Structure Fault Tolerance of Recursive Interconnection Networks

2020 ◽  
Author(s):  
Eminjan Sabir ◽  
Jixiang Meng
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Theoretical Problem ◽  
Connected Subgraph ◽  
Edge Connectivity ◽  
Minimum Cardinality ◽  
Edge Disjoint ◽  
Balanced Hypercube

Abstract Motivated by effects caused by structure link faults in networks, we study the following graph theoretical problem. Let $T$ be a connected subgraph of a graph $G$ except for $K_{1}$. The $T$-structure edge-connectivity $\lambda (G;T)$ (resp. $T$-substructure edge-connectivity $\lambda ^s(G;T)$) of $G$ is the minimum cardinality of a set of edge-disjoint subgraphs $\mathcal{F}=\{T_{1},T_{2},\ldots ,T_{m}\}$ (resp. $\mathcal{F}=\{T_{1}^{^{\prime}},T_{2}^{^{\prime}},\ldots ,T_{m}^{^{\prime}}\}$) such that $T_{i}$ is isomorphic to $T$ (resp. $T_{i}^{^{\prime}}$ is a connected subgraph of $T$) for every $1 \le i \le m$, and $E(\mathcal{F})$’s removal leaves the remaining graph disconnected. In this paper, we determine both $\lambda (G;T)$ and $\lambda ^{s}(G;T)$ for $(1)$ the hypercube $Q_{n}$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},P_{4},Q_{1},Q_{2},Q_{3}\}$; $(2)$ the $k$-ary $n$-cube $Q^{k}_{n}$$(k\ge 3)$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},Q^{3}_{1},Q^{4}_{1}\}$; $(3)$ the balanced hypercube $BH_{n}$ and $T\in \{K_{1,1},K_{1,2},BH_{1}\}$. We also extend some known results.

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