On domination multisubdivision number of unicyclic graphs

• Autorzy: Raczek J.

Identyfikatory

DOI

10.7494/OpMath.2018.38.3.409

• Języki publikacji: EN

Abstrakty

EN

The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.

Słowa kluczowe

EN

domination number; domination subdivision number; domination multisubdivision number; trees; unicyclic graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 3
• Strony: 409--425
• Opis fizyczny: BIbliogr. 13 poz.

Twórcy

autor

Raczek J.

• Gdansk University of Technology Department of Technical Physics and Applied Mathematics Narutowicza 11/12, 80-233 Gdańsk, Poland

Bibliografia

• [1] H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622-628.
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• [3] S. Benecke, C. M. Mynhardt, Trees with domination subdivision number one, Australasian J. Combin. 42 (2008), 201-209.
• [4] M. Dettlaff, J. Raczek, J. Topp, Domination subdivision and domination multisubdivision numbers of graphs, to appear in Discuss. Math. Graph Theory.
• [5] O. Favaron, H. Karami, R. Khoeilar, S.M. Sheikholeslami, On the total domination subdivision number in some classes of graphs, Journal od Combinatorial Optimization 20 (2010), 76-84.
• [6] O. Favaron, H. Karami, S.M. Sheikholeslami, Disproof of a conjecture on the subdivision domination number of a graph, Graphs and Combinatorics 24 (2008), 309-312.
• [7] J.H. Hattingh, E.J. Joubert, M. Loizeaux, A.R. Pmmmer, L.C. van der Merwe, Restrained domination in unicyclic graphs, Discuss. Math. Graph Theory 29 (2009), 71-86.
• [8] T.W. Haynes, M.A. Henning, L. Hopkins, Total domination subdivision numbers of trees, Discrete Math. 286 (2004), 195-202.
• [9] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York, 1998.
• [10] N.J. Rad, Characterization of total restrained domination edge critical unicyclic graphs, Australas. J. Combin. 47 (2010), 77-82.
• [11] P. Roushini Leely Pushpama, T.N.M. Malini Mai, Roman domination in unicyclic graphs, Journal of Discrete Mathematical Sciences and Cryptography 15 (2012), 237-257.
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• [13] S. Velammal, Studies in graph theory: covering, independence, domination and related topics, Ph.D. Thesis, Manonmaniam Sundaranar University, Tirunelveli, 1997.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).