Hamiltonian Properties of Bidimensional Compound Networks

With the development of Internet, data centers become more and more important. The scale of data center network expands rapidly, and the requirements for network cost, energy consumption and maintenance are also increasing. This paper studies the Bidimensional Compound Networks (BCN) based on server-centric nodes and cheaper two-port servers. BCN is a hierarchical dual-port server network structure with two dimensions. On each dimension, a high level uses a low level as a unit cluster and connects many clusters at the same level through a complete graph. It has the advantages of easy expansion, low cost, high efficiency, high security, large network scale, small network diameter, high bandwidth and high fault tolerance. This paper mainly uses exhaustive method and mathematical induction to prove the Hamiltonian connectivity of BCN network structure by two dimensions. These studies provide a theoretical basis for the practical application of BCN in data center network construction.