On kernels by monochromatic paths in the corona of digraphs

Iwona Włoch 1
  • 1 Rzeszow University of Technology


In this paper we derive necessary and sufficient conditions for the existence of kernels by monochromatic paths in the corona of digraphs. Using these results, we are able to prove the main result of this paper which provides necessary and sufficient conditions for the corona of digraphs to be monochromatic kernel-perfect. Moreover we calculate the total numbers of kernels by monochromatic paths, independent by monochromatic paths sets and dominating by monochromatic paths sets in this digraphs product.

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  • [1] Frucht R., Harary F., On the corona of two graphs, Aequationes Math., 1970, 4, 322–324 http://dx.doi.org/10.1007/BF01844162

  • [2] Galeana-Sanchez H., Ramirez L.A.J., Monochromatic kernel-perfectness of special classes of digraphs, Discuss. Math. Graph Theory, 2007, 27, 389–400

  • [3] Topp J., Domination independence and irredundance in graphs, Dissertationes Math., Warszawa, 1995

  • [4] Włoch I., On imp-sets and kernels by monochromatic paths of the duplication, Ars Combin., 2007, 83, 93–99

  • [5] Włoch I., On kernels by monochromatic paths in D-join, preprint


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