Fault-Free Hamiltonian Cycles in Faulty Butterfly Graphs
نویسندگان
چکیده
The butterfly graphs were originally defined as the underlying graphs of FFT networks which can perform the fast Fourier transform (FFT) very eficiently. Since butterfly graphs are regular of degree four, it can tolerate at most two edge faults in the worst case in order to establish a Hamiltonian cycle. In this paper, we show that butterfly graphs contain a fault-free Hamiltonian cycle even if it has two random edge faults.
منابع مشابه
Hamiltonian Paths and Cycles in Faulty Burnt Pancake Graphs
Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a fault-free Hamiltonian cycle if the number of faulty elements is no more than n − 2, and it has a fault-free Hamiltonian path between any pair of non-faulty node...
متن کاملA note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges
In the paper “Fault-free Mutually Independent Hamiltonian Cycles in Hypercubes with Faulty Edges” (J. Comb. Optim. 13:153–162, 2007), the authors claimed that an n-dimensional hypercube can be embedded with (n−1−f )-mutually independent Hamiltonian cycles when f ≤ n−2 faulty edges may occur accidentally. However, there are two mistakes in their proof. In this paper, we give examples to explain ...
متن کاملAdjacent Vertices Fault Tolerance Hamiltonian Laceability of Star Graphs
Let Sn be an n-dimensional Star graph. In this paper, we show that Sn − F is Hamiltonian laceable where F is the set of f ≤ (n − 4) pairs of adjacent faulty vertices, Sn − F is Hamiltonian where F is the set of f ≤ (n − 3) pairs of adjacent faulty vertices. We also show that Sn − F is hyper-Hamiltonian laceable where F is the set of f ≤ (n − 4) pairs of adjacent faulty vertices. Applying these ...
متن کاملSelf-spanner graphs
We introduce the (k, `)–self-spanners graphs to model non-reliable interconnection networks. Such networks can be informally characterized as follows: if at most ` edges have failed, as long as two vertices remain connected, the distance between these vertices in the faulty graph is at most k times the distance in the non-faulty graph. By fixing the values k and ` (called stretch factor and fau...
متن کاملLongest paths and cycles in faulty star graphs
In this paper, we investigate the star graph Sn with faulty vertices and/or edges from the graph theoretic point of view. We show that between every pair of vertices with different colors in a bicoloring of Sn, n ≥ 4, there is a fault-free path of length at least n!− 2fv − 1, and there is a path of length at least n!− 2fv − 2 joining a pair of vertices with the same color, when the number of fa...
متن کامل