Peter Whalen

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About

Peter Whalen is a mathematician whose work lies at the intersection of graph theory and robotics, with a particular focus on the deployment of multi-robot systems. His research addresses the fundamental challenge of how to position sensors or robots on a network so that every vertex is covered, even when the robots have limited sensing capabilities. Whalen’s most notable contribution is his work on deploying robots with only two sensors in \(K_{1,6}\)-free graphs—graphs that avoid a specific star-shaped induced subgraph. He proved that, with the exception of eight small graphs, any such graph of minimum degree at least two can be covered using just five distinct sensor labels. This result, first presented in 2013 and refined in a 2015 publication, has garnered over 25 citations, reflecting its significance in the field of distributed robotics and graph labeling. Whalen’s work elegantly bridges abstract graph structure with practical robotic constraints, offering a powerful framework for efficient sensor placement in complex environments. His findings are particularly valuable for researchers designing scalable, resource-limited robotic networks.