Geodesic
(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 359-371

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Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.
Keywords: state splitting, line digraph, kernel, Grundy function, duality 
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     title = {(k,l)-kernels, (k,l)-semikernels, {k-Grundy} functions and duality for state splittings},
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Galeana-Sánchez, Hortensia; Gómez, Ricardo. (k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 359-371. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a11/