Analysis on component connectivity of bubble-sort star graphs and burnt pancake graphs
Discrete Applied Mathematics(2020)
摘要
The ℓ-component connectivity of a graph G, denoted by cκℓ(G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least ℓ components or a graph with fewer than ℓ vertices. This is a natural generalization of the classical connectivity of graphs defined in terms of the minimum vertex-cut. Since this parameter can be used to evaluate the reliability and fault tolerance of a graph G corresponding to a network, determining the exact values of cκℓ(G) is an important issue on the research topic of networks. However, it has been pointed out in Hsu et al. (2012) that determining ℓ-component connectivity is still unsolved in most interconnection networks even for small ℓ’s. Let BSn and BPn denote the n-dimensional bubble-sort star graph and the n-dimensional burnt pancake graph, respectively. In this paper, for BSn, we determine the values: cκ3(BSn)=4n−9 for n⩾3, and cκ4(BSn)=6n−16 and cκ5(BSn)=8n−24 for n⩾4. Similarly, for BPn, we determine the values: cκ3(BPn)=2n−1 and cκ4(BPn)=3n−2 for n⩾4, and cκ5(BPn)=4n−4 for n⩾5.
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关键词
Component connectivity,Cayley graphs,Bubble-sort star graphs,Burnt pancake graph,Fault-tolerance,Reliability
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