# Design and analysis of the rotational binary graph as an alternative to hypercube and Torus

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## Abstract

Network cost is equal to degree × diameter and is one of the important measurements when evaluating graphs. Torus and hypercube are very well-known graphs. When these graphs expand, a Torus has an advantage in that its degree does not increase. A hypercube has a shorter diameter than that of other graphs, because when the graph expands, the diameter increases by 1. Hypercube Q_{n} has 2^{n} nodes, and its diameter is *n*. We propose the rotational binary graph (RBG), which has the advantages of both hypercube and Torus. RBG_{n} has 2^{n} nodes and a degree of 4. The diameter of RBG_{n} would be 1.5*n* + 1. In this paper, we first examine the topology properties of RBG. Second, we construct a binary spanning tree in RBG. Third, we compare other graphs to RBG considering network cost specifically. Fourth, we suggest a broadcast algorithm with a time complexity of 2*n* − 2. Finally, we prove that RBG_{n} embedded into hypercube Q_{n} results in *dilation n*, and *expansion* 1, and *congestion* 7.

## Keywords

Rotational binary graph Graph Interconnection network Torus Hypercube## Notes

### Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03032173).

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