Consensus on Moving Neighborhood Model of Peterson Graph

TL;DR

This paper investigates the consensus problem for multiple agents performing random walks on the Peterson graph, demonstrating that global consensus can be achieved through numerical analysis of their interactions.

Contribution

It introduces a novel framework where agents randomly walk on the Peterson graph and communicate upon meeting, showing consensus is attainable in this setting.

Findings

Global consensus is achievable in the proposed model.

Numerical simulations confirm the effectiveness of the approach.

Abstract

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.