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Seyedi, Narjes, Maimani, Hamid Reza, Tehranian, Abolfazl. (1401). On the total liar's domination of graphs. , 7(2), 169-175. doi: 10.22049/cco.2021.27219.1213
Narjes Seyedi; Hamid Reza Maimani; Abolfazl Tehranian. "On the total liar's domination of graphs". , 7, 2, 1401, 169-175. doi: 10.22049/cco.2021.27219.1213
Seyedi, Narjes, Maimani, Hamid Reza, Tehranian, Abolfazl. (1401). 'On the total liar's domination of graphs', , 7(2), pp. 169-175. doi: 10.22049/cco.2021.27219.1213
Seyedi, Narjes, Maimani, Hamid Reza, Tehranian, Abolfazl. On the total liar's domination of graphs. , 1401; 7(2): 169-175. doi: 10.22049/cco.2021.27219.1213

On the total liar's domination of graphs

Communications in Combinatorics and Optimization
مقاله 14، دوره 7، شماره 2، اسفند 2022، صفحه 169-175    اصل مقاله (363.08 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2021.27219.1213
نویسندگان
Narjes Seyedi1؛ Hamid Reza Maimani* 2؛ Abolfazl Tehranian1
1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Shahid Rajaee Teacher Training University
چکیده
For a graph $G$, a set $L$ of vertices is called a total liar's domination if $|N_G(u)\cap L|\geq 2$ for any $u\in V(G)$ and $|(N_G(u)\cup N_G(v))\cap L|\geq 3$ for any distinct vertices $u,v\in V(G)$. The total liar’s domination number is the cardinality of a minimum total liar’s
dominating set of $G$ and is denoted by $\gamma_{TLR}(G)$. In this paper we study the total liar's domination numbers of join and products of graphs.
کلیدواژه‌ها
Total liar' s domination؛ Join of graphs؛ Graphs products
مراجع
[1] A. Alimadadi, M. Chellali, and D.A. Mojdeh, Liar’s dominating sets in graphs, Discrete Appl. Math. 211 (2016), 204–210.

[2] R. Diestel, Graph Theory, Springer-Verlag, New York, 1997.

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

[4] B.S. Panda and S. Paul, Hardness results and approximation algorithm for total liar’s domination in graphs, J. Comb. Optim. 27 (2014), no. 4, 643–662.

[5] M.L. Roden and P.J. Slater, Liar’s domination and the domination continuum, Congr. Numer. 190 (2008), 77–85.

[6] , Liar’s domination in graphs, Discrete Math. 309 (2009), no. 19, 5884–5890.

[7] P.J. Slater, Liar’s domination, Networks 54 (2009), no. 2, 70–74.

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