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Abstract
The reliability measure of networks is of significant importance to the design and maintenance of networks. Based on connectivity, many refined quantitative indicators for the reliability of network systems have been introduced. The super vertex edge-connectivity and cyclic edge-connectivity, as important parameters to evaluate the robustness of networks, are explored extensively. As a variant of the hypercube Qn, the varietal hypercube VQn has better properties than Qn with the same number of edges and vertices. Wang and Xu have proved that VQn is super vertex-connected for n≥1 and is also super edge-connected if n≠2. In this paper, we use another method to prove these results. Moreover, we also obtain the super restricted connectivity and the cyclic edge-connectivity of the varietal hypercube VQn.
Highlights
In the era of internet-of-things (IoT), wireless sensor networks (WSNs) are utilised in many applications, including smart grids (SGs) [1]
When the number of sensors continues to increase, faulty nodes and faulty links are inevitable in wireless sensor networks, which undoubtedly increase the difficulty of network reliability assessment and will adversely affect its fault tolerance and reliability
Because the topology of network system can usually be represented by a connected graph G = (V ( G ), E( G )), where V ( G ) and E( G ) can be represented as the set of processors and the set of communication links between processors, respectively
Summary
In the era of internet-of-things (IoT), wireless sensor networks (WSNs) are utilised in many applications, including smart grids (SGs) [1]. The biggest disadvantage of connectivity and edge-connectivity in reliability evaluation and fault-tolerant performance of networks is that they all default to a vertex where all adjacent vertices or adjacent edges fail at the same time, which rarely happens in the real world. The minimum size of all h-restricted vertex-cuts (resp., edge-cuts), denoted by κ (h) ( G ) (resp., λ(h) ( G )), is called h-restricted connectivity (resp., edge-connectivity) of the graph G. G is called super restricted vertex (edge)-connected and denoted by super-κ 0 (resp., super-λ0 ), if every minimum restricted edge cut isolates one component of order 2. The h-restricted (edge)-connectivity and super-κ 0 (resp., super-λ0 ) graph for some classic interconnection networks have been investigated recently.
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