Abstract
Connectivity is a significant metric for evaluating the error lenience of an interconnected net G=V,E. In the paper (Fàbrega and Fiol, 1996), the authors addressed the g-extra connectivity which is applied to better measure the consistency and error tolerance of G. As a special Cayley graph, the n-dimensional wheel network CWn has some desirable features. This paper shows that the g-extra connectivity of CWnn≥6 is 6n−12 when g=2.
Highlights
An interconnected net is usually charactered as a graph, whereat each node resembles a CPU and an edge resembles the connection between a couple of CPUs, correspondingly
Connectivity is an important index in evaluating the dependability and error tolerance of an IN. e greater the connectivity is, the more consistent an IN is
An understandable drawback of the index is that it adopts that each node neighboring the same node of G can flop simultaneously
Summary
An interconnected net (abbreviated IN) is usually charactered as a graph, whereat each node (vertex) resembles a CPU and an edge resembles the connection between a couple of CPUs, correspondingly. The traditional connectivity is inappropriate for huge computing systems To overcome this deficiency, Harary [1] firstly presented the idea of restricted connectivity, which is a more refined index in determining the consistency and error tolerance of INs. Consider G to be a linked directionless basic graph, and p be a given 1-dimensional topology theory feature. E restricted connectivity, written as κ(G; p), is obtained as the minimum cardinality of a set of nodes, if any, whose deletion detaches G and each residual factor has feature p. E g-extra connectivity of G, if there must exist 1 g-extra cut, written as κ(g)(G), is obtained as the minimum cardinality above all g-extra cuts of G, namely, κ(g)(G) κ(G; pg), whereat pg is the feature that each residual element takes at least (g + 1) nodes. We establish that the g-extra connectivity of CWn(n ≥ 6) is 6n − 12, when g 2
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