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I will talk about highly symmetric colorings of highly symmetric graphs. With many
examples, we will discuss how to find such colorings, how to show non-isomorphism, and we
will see some of the varieties of such colorings. Most importantly, we will see how understanding
the colorings of a graph helps to understand its structure.

Underwater gliders, propeller-driven submersibles, and other marine robots are increasingly being tasked with gathering information (e.g., in environmental monitoring, offshore inspection, and coastal surveillance scenarios). However, in most of these scenarios, human operators must carefully plan the mission to ensure completion of the task. Strict human oversight not only makes such deployments expensive and time consuming but also makes some tasks impossible due to the requirement for heavy cognitive loads or reliable communication between the operator and the vehicle.