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γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 اردیبهشت 1403 اصل مقاله (428.72 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2024.27940.1401 | ||
نویسندگان | ||
Pannawat Eakawinrujee؛ Nantapath Trakultraipruk* | ||
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand | ||
چکیده | ||
A total dominating set of a graph $G$ is a set $D\subseteq V(G)$ such that every vertex of $G$ is adjacent to some vertex in $D$. The total domination number $\gamma_{t}(G)$ of $G$ is the minimum cardinality of a total dominating set. The $\gamma$-total dominating graph $TD_{\gamma}(G)$ of $G$ is the graph whose vertices are minimum total dominating sets, and two minimum total dominating sets of $TD_{\gamma}(G)$ are adjacent if they differ by only one vertex. In this paper, we determine the total domination numbers of lollipop graphs, umbrella graphs, and coconut graphs, and especially their $\gamma$-total dominating graphs. | ||
کلیدواژهها | ||
total domination number؛ total dominating graph؛ gamma graph | ||
مراجع | ||
[1] S. Alikhani, D. Fatehi, and C.M. Mynhardt, On $k$-total dominating graphs, Australas. J. Combin. 73 (2019), no. 2, 313––333.
[2] A. Bień, Gamma graphs of some special classes of trees, Ann. Math. Sil. 29 (2015), no. 1, 25––34. https://doi.org/10.1515/amsil-2015-0003 [3] E.J. Cockayne, R.M. Dawes, and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1998), no. 3, 211–219. https://doi.org/10.1002/net.3230100304 [4] E. Connelly, K.R. Hutson, S.T. Hedetniemi, and T.W. Haynes, A note on $\gamma$-graphs, AKCE Int. J. Graphs Comb. 8 (2011), no. 1, 23–31.
[5] P. Eakawinrujee and N. Trakultraipruk, $\gamma$-paired dominating graphs of cycles, Opusc. Math. 42 (2022), no. 1, 31–54. https://doi.org/10.7494/OpMath.2022.42.1.31 [6] P. Eakawinrujee and N. Trakultraipruk, $\gamma$-paired dominating graphs of paths, Int. J. Math. Comput. Sci. 17 (2022), no. 2, 739–752.
[7] P. Eakawinrujee and N. Trakultraipruk, $\gamma$-paired dominating graphs of lollipop, umbrella and coconut graphs, Electron. J. Graph Theory Appl. 11 (2023), no. 1, 65–79. http://dx.doi.org/10.5614/ejgta.2023.11.1.6 [8] D. Fatehi, S. Alikhani, and A.J.M. Khalaf, The $k$-independent graph of a graph, Adv. Appl. Discrete Math. 18 (2017), no. 1, 45–56. http://dx.doi.org/10.17654/DM018010045 [9] G. Fricke, S. Hedetniemi, S. Hedetniemi, and K. Hutson, γ-graphs of graphs, Discuss. Math. Graph Theory 31 (2011), no. 3, 517–531. https://doi.org/10.7151/dmgt.1562 [10] R. Haas and K. Seyffarth, The $k$-dominating graph, Graphs Combin. 30 (2014), 609–617. https://doi.org/10.1007/s00373-013-1302-3 [11] R. Haas and K. Seyffarth, Reconfiguring dominating sets in some well-covered and other classes of graphs, Discrete Math. 340 (2017), no. 8, 1802–1817. https://doi.org/10.1016/j.disc.2017.03.007 [12] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
[13] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. [14] M.A. Henning, Graphs with large total domination number, J. Graph Theory 35 (2000), no. 1, 21–45.
[15] S.A. Lakshmanan, A. Vijayakumar, and S. Arumugam, The gamma graph of a graph, AKCE Int. J. Graphs Comb. 7 (2010), no. 1, 53–59.
[16] C.M. Mynhardt, A. Roux, and L.E. Teshima, Connected $k$-dominating graphs, Discrete Math. 342 (2019), no. 1, 145–151. https://doi.org/10.1016/j.disc.2018.09.006 [17] C.M. Mynhardt and L.E. Teshima, A note on some variations of the γ-graph, J. Comb. Math. Comb. Comput. 104 (2018), 217—-230.
[18] R. Samanmoo, N. Trakultraipruk, and N. Ananchuen, $\gamma$-independent dominating graphs of paths and cycles, Maejo Int. J. Sci. Technol. 13 (2019), no. 3, 245–256.
[19] S. Sanguanpong and N. Trakultraipruk, $\gamma$-induced-paired dominating graphs of paths and cycles, Discrete Math. Algorithms Appl. 14 (2022), no. 8, Article ID: 2250047. https://doi.org/10.1142/S1793830922500471 | ||
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