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Monophonic eccentric domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 9، شماره 4، اسفند 2024، صفحه 625-633 اصل مقاله (393.29 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28156.1460 | ||
| نویسندگان | ||
| P. Titus* 1؛ J. Ajitha Fancy2 | ||
| 1Department of Mathematics, University College of Engineering Nagercoil, Anna University, Tirunelveli Region, Nagercoil - 629 004, India | ||
| 2Department of Mathematics, Scott Christian College (Autonomous), Nagercoil - 629 003, India | ||
| چکیده | ||
| For any two vertices $u$ and $v$ in a connected graph $G,$ the monophonic distance $d_m(u,v)$ from $u$ to $v$ is defined as the length of a longest $u-v$ monophonic path in $G$. The monophonic eccentricity $e_m(v)$ of a vertex $v$ in $G$ is the maximum monophonic distance from $v$ to a vertex of $G$. A vertex $v$ in $G$ is a monophonic eccentric vertex of a vertex $u$ in $G$ if $e_m(u) = d_m(u,v)$. A set $S \subseteq V$ is a monophonic eccentric dominating $set$ if every vertex in $V-S$ has a monophonic eccentric vertex in $S$. The monophonic eccentric domination number $\gamma_{me}(G)$ is the cardinality of a minimum monophonic eccentric dominating set of $G$. We investigate some properties of monophonic eccentric dominating sets. Also, we determine the bounds of monophonic eccentric domination number and find the same for some standard graphs. | ||
| کلیدواژه‌ها | ||
| monophonic path؛ monophonic distance؛ monophonic eccentric vertex؛ monophonic eccentric dominating set؛ monophonic eccentric domination number | ||
| مراجع | ||
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[1] C. Berge, Theory of Graphs and its Applications, Methuen, London, 1962.
[2] M. Bhanumathi and R.M. Abirami, Superior eccentric domination in graphs, Int. J. Pure Appl. Math. 117 (2017), no. 14, 175–182.
[3] M. Bhanumathi and R.M. Abirami, Upper eccentric domination in graphs, J. Discrete Math. Sci. Crypt. 22 (2019), no. 5, 835–846. https://doi.org/10.1080/09720529.2019.1685236
[4] G. Chartrand, T.W. Haynes, M.A. Henning, and P. Zhang, Detour domination in graphs, Ars Combin. 71 (2004), 149–160.
[5] F. Harary, Graph Theory, Addison-Wesley, 1969.
[6] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
[7] A.M. Ismayil and R. Priyadharshini, Detour eccentric domination in graphs, Bull. Pure Appl. Sci. 38E (2019), no. 1, 342–347.
[8] A.M. Ismayil and A.R.U. Rehman, Accurate eccentric domination in graphs, Our Heritage 68 (2020), no. 4, 209–216.
[9] A.M. Ismayil and A.R.U. Rehman, Equal eccentric domination in graphs, Malaya J. Mat. 8 (2020), no. 1, 159–162.
[10] R. Jahir Hussain and A. Fathima Begam, Inverse eccentric domination in graphs, Adv. Appl. Math. Sci. 20 (2021), no. 4, 641–648.
[11] T.N. Janakiraman, M. Bhanumathi, and S. Muthammai, Eccentric domination in graphs, Int. J. Eng. Sci. Adv. Comput. Bio Tech. 1 (2010), no. 2, 55–70.
[12] K.S.J. Kalaiarasan and K.L. Gipson, Eccentric domination decomposition of graphs, Malaya J. Mat. 8 (2020), no. 3, 1186–1188.
[13] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ., 1962.
[14] A. Prasanna and N. Mohamedazarudeen, D–eccentric domination in graphs, Adv. Appl. Math. Sci. 20 (2021), no. 4, 541–548.
[15] A.P. Santhakumaran and P. Titus, Monophonic distance in graphs, Discrete Math. Algorithms Appl. 3 (2011), no. 2, 159–169. https://doi.org/10.1142/S1793830911001176
[16] A.P. Santhakumaran and P. Titus, A note on “Monophonic distance in graphs”, Discrete Math. Algorithms Appl. 4 (2012), no. 2, Article ID: 1250018. https://doi.org/10.1142/S1793830912500188 [17] P. Titus and J.A. Fancy, Connected total monophonic eccentric domination in graphs, preprint.
[18] P. Titus and J.A. Fancy, Total monophonic eccentric domination in graphs, communicated.
[19] P. Titus and J.A. Fancy, Total monophonic eccentric domination number of corona product of some standard graphs, Tierärztliche Praxis 40 (2020), 493– 508. | ||
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