Temporal graphs are graphs where the presence or properties of their vertices and edges change over time. When time is discrete, a temporal graph can be defined as a sequence of static graphs over a discrete time span, called lifetime, or as a single graph where each edge is associated with a specific set of time instants where the edge is alive. For static graphs, Courcelle’s Theorem asserts that any graph problem expressible in monadic second-order logic can be solved in linear time on graphs of bounded tree-width. We propose the first adaptation of Courcelle’s Theorem for monadic second-order logic on temporal graphs that does not explicitly rely on a parameter proportional to the lifetime, or defined as the maximum number of time-edges incident with any vertex which in the worst case is higher than the lifetime. We then introduce the notion of derivative over a sliding time window of a chosen size, and define the tree-width and twin-width of the temporal graph’s derivative. We exemplify its usefulness with meta-theorems with respect to a temporal variant of first-order logic. The resulting logic expresses a wide range of temporal graph problems including a version of temporal cliques, an important notion when querying time series databases for community structures.

This paper presents a decentralized leader election algorithm for unmanned aerial vehicle (UAV) swarms operating under Optical Wireless Communication (OWC) constraints. To enable interference-free, RF-independent coordination, the method unifies swarm initialization and navigation planning. Each UAV relies solely on local sensing and directional laserdiode communication without centralized control. Leadership is determined from a multi-criteria score combining compactness, neighborhood size, target proximity, and angular dispersion, followed by distributed conflict resolution and follower assignment. Large-scale simulations, up to 5000 UAVs, demonstrate full coverage, stable leader-follower structures, and high leadership quality with low communication overhead, confirming the scalability and robustness of the approach.