# A combinatorial approach to counting primitive periodic and primitive pseudo orbits on circulant graphs

@inproceedings{Engelthaler2021ACA, title={A combinatorial approach to counting primitive periodic and primitive pseudo orbits on circulant graphs}, author={Lauren Engelthaler and Isaac Hellerman and Tori Hudgins}, year={2021} }

We count the numbers of primitive periodic orbits on families of 4-regular directed circulant graphs with n vertices. The relevant counting techniques are then extended to count the numbers of primitive pseudo orbits (sets of distinct primitive periodic orbits) up to length n that lack self-intersections, or that never intersect at more than a single vertex at a time repeated exactly twice for each self-intersection (2-encounters of length zero), for two particular families of graphs. We then… Expand

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