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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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[1] F. Buckley and F. Harary, Distance in Graph, Addition-Wesley-Wood City, CA, 1990. [2] E. J. Cockayne, O. Favaron and C. M. Mynhardt, Secure domination, weak roman domination and forbidden subgraph, Bull. Inst. Combin. Appl., 39 (2003), 87-100. [3] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. [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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