Consensus on Moving Neighborhood Model of Peterson Graph

In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if and only if they coincide on a node at the same time. We conduct numerical study on the consensus problem in this framework and show that global consensus can be achieved.

💡 Research Summary

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The paper investigates a consensus problem for multiple autonomous agents moving on the Petersen graph, a well‑known undirected graph with ten vertices and fifteen edges. Each agent performs an independent random walk on the graph, selecting a neighboring vertex uniformly at random at each discrete time step. Communication between agents is extremely limited: two agents can exchange information only when they occupy the same vertex at the same instant. The authors adopt a standard linear consensus protocol in discrete time:

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