Double Total Domination in Harary Graphs

Authors

  • Adel P. Kazemi Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 5619911367, Ardabil
  • Behnaz Pahlavsay Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 5619911367, Ardabil

DOI:

https://doi.org/10.26713/cma.v8i1.701

Keywords:

Double total domination number, Harary graph

Abstract

Let \(G\) be a graph with minimum degree at least 2. A set \(D\subseteq V\) is a double total dominating set of \(G\) if each vertex is adjacent to at least two vertices in \(D\). The double total domination number \(\gamma _{\times 2,t}(G)\) of \(G\) is the minimum cardinality of a double total dominating set of \(G\). In this paper, we will find double total domination number of Harary graphs.

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References

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York (1998).

T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.), Domination in Graphs: Advanced Topics, Marcel Dekker, Inc., New York (1998).

M.A. Henning and A.P. Kazemi, k-tuple total domination in graphs, Discrete Applied Mathematics 158 (2010), 1006 – 1011.

M.A. Henning and A.P. Kazemi, k-tuple total domination in cross product of graphs, J. Comb. Optim. 24 (3) (2012), 339 – 346.

A.P. Kazemi, k-tuple total domination in complementary prismss, ISRN Discrete Mathematics 2011, article ID 681274 (2011), doi:10.5402/2011/681274.

A.P. Kazemi and B. Pahlavsay, k-tuple total domination in Supergeneralized Petersen graphs, Communications in Mathematics and Applications 2 (1) (2011), 21 – 30.

D.B. West, Introduction to Graph Theory, 2nd edition, Prentice Hall USA (2001).

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Published

30-06-2017
CITATION

How to Cite

Kazemi, A. P., & Pahlavsay, B. (2017). Double Total Domination in Harary Graphs. Communications in Mathematics and Applications, 8(1), 1–6. https://doi.org/10.26713/cma.v8i1.701

Issue

Vol. 8 No. 1 (2017)

Section

Research Article

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