Opuscula Math. 36, no. 5 (2016), 575-588
http://dx.doi.org/10.7494/OpMath.2016.36.5.575

Opuscula Mathematica

# Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

Magda Dettlaff
Joanna Raczek
Ismael G. Yero

Abstract. Given a graph $$G=(V,E)$$, the subdivision of an edge $$e=uv\in E(G)$$ means the substitution of the edge $$e$$ by a vertex $$x$$ and the new edges $$ux$$ and $$xv$$. The domination subdivision number of a graph $$G$$ is the minimum number of edges of $$G$$ which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of $$G$$ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.

Keywords: domination, paired domination, independent domination, edge subdivision, edge multisubdivision, corona graph.

Mathematics Subject Classification: 05C69, 05C70, 05C76.

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• Magda Dettlaff
• Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland
• Joanna Raczek
• Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland
• Ismael G. Yero
• Universidad de Cádiz, Escuela Politécnica Superior de Algeciras, Departamento de Matemáticas, Av. Ramón Puyol, s/n, 11202 Algeciras, Spain
• Communicated by Dalibor Fronček.
• Revised: 2016-05-08.
• Accepted: 2016-05-10.
• Published online: 2016-06-29.