About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs
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Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 = l = k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial linedigraph LD. Moreover, if l < k and the girth of D is at least l+1, then these two numbers are equal. We also prove that the number of semikernels of D is equal to the number of semikernels of LD. Furthermore, we introduce the concept of (k, l)-Grundy function as a generalization of the concept of Grundy function and we prove that the number of (k, l)-Grundy functions of D is equal to the number of (k, l)-Grundy functions of any partial line digraph LD.
CitationBalbuena, C.; Galeana, H.; Guevara, N. About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs. "Discussiones Mathematicae Graph Theory", Juny 2019, vol. 39, núm. 4, p. 855-866.
ISSNISSN 1234-3099 (print version) ISSN 2083-5892 (electronic version)
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