Circulant Graphs: Symmetry on a Circle

In this Deep Dive, we explore circulant graphs—the highly symmetric networks that stay the same under rotation. We'll unpack multiple equivalent definitions (automorphism groups, circulant adjacency matrices, modular difference labeling, and geometric/Cayley perspectives), visualize them on a circle, and survey familiar examples such as cycle graphs, Paley graphs, Mobius ladders, and rook graphs. If you like symmetry at the intersection of algebra, geometry, and graph theory, this episode is for you.

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