• D. Josephine Divya
• Dr. K. Sunitha

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 f∈VM there exists g∈M such that f is adjacent to g and S_m=(M {g} )∪{f} is a monophonic dominating set. A secure monophonic dominating set S_m is said to be a secure monophonic global domination set (abbreviated as SMGD set) of G if S_m is a global dominating set of G. A secure monophonic dominating set S_m is called a total secure monophonic dominating set T_sm ( abbreviated as TSMD set ) of G if for every vertex of g∈V, there exists a vertex f∈T_sm, f≠g, such that f is adjacent to g. The minimum cardinality of a SMGD set and TSMD set of G is the SMGD number and TSMD number of G and is denoted by γ ̅ₛₘ(G) and γ_tsm (G) respectively

Monophonic path, Secure monophonic global domination number, Total secure monophonic domination number.

"Secure Monophonic Global Domination number and Total Secure Monophonic Domination Number of Subdivision of Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 11, page no.f432-f435, November-2025, Available :http://www.jetir.org/papers/JETIR2511572.pdf

"Secure Monophonic Global Domination number and Total Secure Monophonic Domination Number of Subdivision of Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 11, page no. ppf432-f435, November-2025, Available at : http://www.jetir.org/papers/JETIR2511572.pdf