• T.Premala
• N.Jemima Christabel
• S.Thiruvazhimarbapillai

Let G=(V,E) be a simple graph. A set S⊆V is a total dominating set of G if every vertex is adjacent to an element of S. Let D_t (S_n,i) be the family of all total dominating set of the graph S_n ,n≥2 with cardinality i, and let d_t (S_n,i) = 〖│D〗_t (S_n,i)│.In this paper we construct d_t (S_n,i), and obtain the polynomial D_t (S_n,x)= ∑_(i=Υ_t (S_n))^n▒〖d_t (S_n,i)x^i 〗 ,which we call total domination polynomial of S_n ,n≥2 and obtain some properties of this polynomial.

Star graph, Total dominating set, Total domination polynomial

"Total Dominating sets and Total Domination Polynomials of Star Graph", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 1, page no.g728-g734, January-2024, Available :http://www.jetir.org/papers/JETIR2401684.pdf

"Total Dominating sets and Total Domination Polynomials of Star Graph", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 1, page no. ppg728-g734, January-2024, Available at : http://www.jetir.org/papers/JETIR2401684.pdf