Reliability Analysis of Varietal Hypercube
- 1 Department of Mathematics, Qinghai Nationalities University, Xining, China
- 2 Department of Mathematics, Qinghai Nationalities University, Xining, China
- 3 Department of Mathematics, Qinghai Nationalities University, Xining, China
Abstract
Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let <img src="https://html.scirp.org//file/7405236-rId12.svg?20240412025834" > be a connected graph. A connected graph <i>G</i> is called supper-<i>κ </i>(resp. supper-<i>λ</i>) if every minimum vertex cut (edge cut) of <i>G</i> is the set of neighbors of some vertex in <i>G</i>. The <i>g</i>-component connectivity of a graph <i>G</i>, denoted by <img src="https://html.scirp.org//file/7405236-rId14.svg?20240412025834" >, is the minimum number of vertices whose removal from <i>G</i> results in a disconnected graph with at least <i>g</i> components or a graph with fewer than <i>g</i> vertices. The <i>g</i>-component edge connectivity <img src="https://html.scirp.org//file/7405236-rId16.svg?20240412025834" > can be defined similarly. In this paper, we determine the <i>g</i>-component (edge) connectivity of varietal hypercube <img src="https://html.scirp.org//file/7405236-rId18.svg?20240412025834" > for small <i>g</i>.
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