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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 | ||
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[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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