On kernels by monochromatic paths in the corona of digraphs

Iwona Włoch

Open Mathematics (2008)

  • Volume: 6, Issue: 4, page 537-542
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Iwona Włoch. "On kernels by monochromatic paths in the corona of digraphs." Open Mathematics 6.4 (2008): 537-542. <http://eudml.org/doc/269242>.

@article{IwonaWłoch2008,
abstract = {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.},
author = {Iwona Włoch},
journal = {Open Mathematics},
keywords = {kernel by monochromatic paths; corona; counting; corona of digraphs; monochromatic kernel-perfect},
language = {eng},
number = {4},
pages = {537-542},
title = {On kernels by monochromatic paths in the corona of digraphs},
url = {http://eudml.org/doc/269242},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Iwona Włoch
TI - On kernels by monochromatic paths in the corona of digraphs
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 537
EP - 542
AB - 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.
LA - eng
KW - kernel by monochromatic paths; corona; counting; corona of digraphs; monochromatic kernel-perfect
UR - http://eudml.org/doc/269242
ER -

References

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  1. [1] Frucht R., Harary F., On the corona of two graphs, Aequationes Math., 1970, 4, 322–324 http://dx.doi.org/10.1007/BF01844162 Zbl0198.29302
  2. [2] Galeana-Sanchez H., Ramirez L.A.J., Monochromatic kernel-perfectness of special classes of digraphs, Discuss. Math. Graph Theory, 2007, 27, 389–400 Zbl1142.05037
  3. [3] Topp J., Domination independence and irredundance in graphs, Dissertationes Math., Warszawa, 1995 Zbl0830.05052
  4. [4] Włoch I., On imp-sets and kernels by monochromatic paths of the duplication, Ars Combin., 2007, 83, 93–99 Zbl1174.05114
  5. [5] Włoch I., On kernels by monochromatic paths in D-join, preprint 

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