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Sunitha, K, Divya, D. (1403). Secure monophonic domination of graphs. سامانه مدیریت نشریات علمی, 13(2), 247-256. doi: 10.22098/jhs.2024.16053.1057
K Sunitha; D Josephine Divya. "Secure monophonic domination of graphs". سامانه مدیریت نشریات علمی, 13, 2, 1403, 247-256. doi: 10.22098/jhs.2024.16053.1057
Sunitha, K, Divya, D. (1403). 'Secure monophonic domination of graphs', سامانه مدیریت نشریات علمی, 13(2), pp. 247-256. doi: 10.22098/jhs.2024.16053.1057
Sunitha, K, Divya, D. Secure monophonic domination of graphs. سامانه مدیریت نشریات علمی, 1403; 13(2): 247-256. doi: 10.22098/jhs.2024.16053.1057

Secure monophonic domination of graphs

Journal of Hyperstructures
دوره 13، شماره 2، 2024، صفحه 247-256    اصل مقاله (1.58 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22098/jhs.2024.16053.1057
نویسندگان
K Sunitha1؛ D Josephine Divya* 2
1Department of Mathematics, Scott Christian College(Autonomous), Nagercoil, India
2Devasahayam Mount, Aralvaimozhi
چکیده
Let G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set Sm (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and Sm = {M \(u)} ∪{v} is a monophonic dominating set. The minimum cardinality of a secure monophonic dominating set of G is the secure monophonic domination number of G and is denoted by γsm(G). In this paper, we investigate the secure monophonic domination number of subdivision of graphs such as subdivision of Path graph S(Pn), subdivision of Cycle graph S(Cn), subdivision of Star graph S(K1,n-1), subdivision Bistar graph S(Bm,n) and subdivision of Y-tree graph S(Yn+1).
کلیدواژه‌ها
Monophonic path؛ Monophonic domination number؛ Secure mono- phonic domination number
مراجع
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[4] J. John and P. Arul Paul Sudhahar, The monophonic domination number of a graph, Proceedings of the International Conference on Mathematics and Business Management, 1 (2012), 142-145.
[5] S. M. Mirafzal, Some algebraic properties of the subdivision graph of a graph, Communications in Combinatorics and Optimization, 9(2) (2024), 297-307.
[6] M. Kamran Siddiqui, On edge irregularity strength of subdivision of star Sn, International Journal of Mathematics and Soft Computing, 2(1) (2012), 75-82.
[7] A. Nellai Murugan and J. Shiny Priyanka, Tree Related Extended Mean Cordial Graphs, International Journal of Research-Granthaalayah, 3(9) (2015), 43-148.
[8] K. Praveena, M. Venkatachalam and A. Rohini, Equitable coloring on subdivision vertex join of cycle Cm with path Pn, Notes on Number theory and Discrete Mathematics, 25(2) (2019, 190-198.
[9] K. Sunitha and M. Sheriba, Gaussian Tribonacci R-Gracefull labeling of some tree related graphs, Ratio Mathematics journal, 44 (2022), 188-196.
[10] K. Sunitha and D. Josephine Divya, Secure monophonic domination number of graphs and its complement, ICAMD-2024 Proceedings.

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