Embedding Hierarchical Fibonacci Cubes In Faulty Hierarchic Cubic Networks

Abstract

Hierarchical Fibonacci Cubes HFC(n+2) can be obtained from the Hierarchic Cubic Network HCN(n,n) by removing certain nodes and edges. This problem is very simple when no faulty node exists in an HCN(n,n), however, it becomes very sophisticated if some faulty nodes appear in an HCN(n,n). In this paper, we tried to distinguish HFC(n+2) in faulty HCN(n,n), and it can also be considered as a fault-tolerant embedding in HCN(n,n). Then, we shall show how to dierctly embed a HFC(n+2) into a faulty HCN(n,n) and prove that if no more than two clusters which contain faulty nodes, then HFC(n+2) can be directly embedded. Another case is that if there are more than two clusters which contain faulty nodes, then the labels of faulty nodes must be (I_i,K) and (I_i,L) for each cluster.

Keywords

• Hierarchical Cubic Network - HCN(n,n),Hierarchical Fibonacci Cube – HFC(n)

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