Abstract
The interconnection network is an essential component of a distributed system or of a supercomputer based on large-sale parallel processing. Because in distributed systems the communication between processors is based on message exchange, the network topology is of a great importance. The interconnection network can be seen as a graph and the properties of a network can be studied using combinatorics and graph theory. A number of interconnection network topologies have been studied. The Extended Fibonacci Cube, EFC, is a topology which provides good properties for an interconnection network regarding diameter, node degree, recursive decomposition, embeddability and communication algorithms. In this research we present some properties of the Extended Fibonacci Cubes, we define a Gray code for extended Fibonacci cubes and show how a hamiltonian path, a hamiltonian cycle and a 2D mesh can be embedded in an Extended Fibonacci Cube.
Highlights
An interconnection network consists of a set of processors, each with a local memory and a set of bidirectional links that serve for the exchange of data between processors
Because in distributed systems the communication between processors is based on message exchange, the network topology is of a great importance
In this research we present some properties of the Extended Fibonacci Cubes, we define a Gray code for extended Fibonacci cubes and show how a hamiltonian path, a hamiltonian cycle and a 2D mesh can be embedded in an Extended Fibonacci Cube
Summary
An interconnection network consists of a set of processors, each with a local memory and a set of bidirectional (or unidirectional) links that serve for the exchange of data between processors. Some of the key features of interest in such an interconnection network are its topological properties as node degree, diameter, connectivity, structure, the embeddability of other topologies and the communication algorithms. A widely studied interconnection topology is the hypercube, or the ncube Hn. The hypercube has good properties such as symmetry, small diameter and node degree, recursive structure, efficient communication algorithms. Hsu[5] proposed and studied the properties of a new interconnection topology called Fibonacci cube based on the Fibonacci numbers. The Extended Fibonacci Cubes are defined using the same recursive relation as the Fibonacci numbers, but changing the initial conditions. In this way the number of choices for the number of nodes for an interconnection network increases. In this research we will define a Gray code for extended Fibonacci cubes and using this code we will define a hamiltonian path in an extended Fibonacci cube
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
