G. Stacey Staples
ABSTRACT
Nilpotent adjacency matrix methods (based on zeon algebras) are extended to graph processes (i.e., sequences of colored graphs) by defining sequences of "zeon edge-coloring matrices" whose entries come from a particular commutative subalgebra of a Clifford algebra of appropriate signature. By utilizing orthozeons, enumeration of monochromatic paths in colored graph processes is possible. Introduced here are the "path-identifying orthozeons", whose properties allow the enumeration of monochromatic paths in edge-colored graphs. The algebraic formalism lends itself well to symbolic computations in Mathematica.
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Index Terms
- Zeons, orthozeons, and processes on colored graphs
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