University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 13 2 2024 12 01 Secure monophonic domination of graphs 247 256 3547 10.22098/jhs.2024.16053.1057 EN K Sunitha Department of Mathematics, Scott Christian College(Autonomous), Nagercoil, India D Josephine Divya Devasahayam Mount, Aralvaimozhi Journal Article 2024 10 22 Let G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set S<sub>m</sub> (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and S<sub>m</sub> = {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 γ<sub>sm</sub>(G). In this paper, we investigate the secure monophonic domination number of subdivision of graphs such as subdivision of Path graph S(P<sub>n</sub>), subdivision of Cycle graph S(C<sub>n</sub>), subdivision of Star graph S(K<sub>1,n-1</sub>), subdivision Bistar graph S(B<sub>m,n</sub>) and subdivision of Y-tree graph S(Y<sub>n+1</sub>). Monophonic path Monophonic domination number Secure mono- phonic domination number https://jhs.uma.ac.ir/article_3547_cbbf01bc4e292c3dd405e680fd1a9eb6.pdf