Embedding Hierarchical Fibonacci Cubes In Faulty Hierarchic Cubic Networks

Year 2016, Volume: 1 Issue: 1, 14 - 19, 01.12.2016

Ali Karcı

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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