Expanded Borel Cayley Graphs (Ex-BCGs): A novel communication topology for multi-agent systems

In our early ork, e reported Borel Cayley Graphs (BCGs) have the best topological and graph-spectral properties compared to toroidal and diagonal mesh networks and small-orld networks. Hoever, BCGs' dependence on generating parameters in size selection and network characteristics has been a challenge in network applications. In this paper, e propose Expanded Borel Cayley Graphs (Ex-BCGs) as a communication topology for multi-agent systems. Ex-BCGs are group-theoretically expanded graphs from BCGs ith fixed generating parameters. Ex-BCGs not only conserve constant nodal degree and node labeling scheme but also inherit the communication efficiency of the original BCGs. ith experimental results, e sho the proposed Ex-BCGs no longer require ne generating parameters for ne sizes. Moreover, e sho resolution of this constraint to produce efficient topological and graph-spectral properties and fast convergence speed hen compared to BCGs of similar sizes. e also present the Cut-Through Reiring (CTR) algorithm as a fault-tolerant methodology against node-failures by regarding pruning nodes as node-failures and utilizing the CTR as a ay of recovering connections for neighbors of the pruned nodes in multi-agent systems. The numerical results sho that resized networks from Ex-BCGs by the CTR algorithm are more fault-tolerant ith robust connectivity, efficient topological properties and faster convergence speed than BCGs.