A new hypercube variant: Fractal Cubic Network Graph

Abstract

Hypercube is a popular and more attractive interconnection networks. The attractive properties of hypercube caused the derivation of more variants of hypercube. In this paper, we have proposed two variants of hypercube which was called as “Fractal Cubic Network Graphs”, and we have investigated the Hamiltonian-like properties of Fractal Cubic Network Graphs FCNGr(n). Firstly, Fractal Cubic Network Graphs FCNGr(n) are defined by a fractal structure. Further, we show the construction and characteristics analyses of FCNGr(n) where r=1 or r=2. Therefore, FCNGr(n) is a Hamiltonian graph which is obtained by using Gray Code for r=2 and FCNG1(n) is not a Hamiltonian Graph. Furthermore, we have obtained a recursive algorithm which is used to label the nodes of FCNG2(n). Finally, we get routing algorithms on FCNG2(n) by utilizing routing algorithms on the hypercubes.

Keywords

• Hamiltonian graph
• Eulerian graph
• Gray code
• Interconnection network
• Fractal Cubic Network Graph