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Zeons, Orthozeons, and Graph Colorings
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| Advances in Applied Clifford Algebras |
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Nilpotent adjacency matrix methods have proven useful for counting self-avoiding walks (paths, trails, cycles, and circuits) in finite graphs. In the current work, these methods are extended for the first time to problems related to graph colorings. Nilpotent-algebraic formulations of graph coloring problems include necessary and sufficient conditions for k-colorability, enumeration (counting) of heterogeneous and homogeneous paths, trails, cycles, and circuits in colored graphs, and a matrix-based greedy coloring algorithm. Introduced here also are the orthozeons and their application to counting monochromatic selfavoiding walks in colored graphs. The algebraic formalism easily lends itself to symbolic computations, and Mathematica-computed examples are presented throughout.
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