The restricted connectivity of complete-transposition networks
Complete-transposition networks are a class of important Cayley graphs in networks design.The k-restricted vertex(edge)-connectivity of a graph G is the minimum cardinality of a set of vertices (edges) in G whose removal results in disconnected and each component has at least k vertices,denoted by κk(λk).The k-restricted vertex(edge)-connectivity is one of the most parameters to evaluate the reliability of a network,it is also a refined measure of the fault tolerance of the graph.In general,the larger the k-restricted vertex(edge)-connectivity of a network,the more reliable the network.The paper proves that 2-restricted vertex(edge)-connectivity and 3-restricted vertex(edge)-connectivity of complete-transposition networks,that is,when n ≥ 4,κ2 (CT,n) =n (n-1)-2,κ3 (CT,n) =3n(n-n)/2-6,when n ≥ 3,λ2(CT,n) =n(n-1)-2,λ3(CT,n) =3n(n-1)/2-4.
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