Total Dominating Sets and Total Domination Polynomials of Square Of Paths
T Premala, C. Sekar · IOSR Journal of Mathematics · 2014
Let G= ( V , E ) be a simple connected 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 (P n 2 ,i) be the family of all total dominating sets of the graph P n 2 ,n ≥ 2 with cardinality i, and let d t (P n 2 ,i) =│D t (P n 2 ,i)│.In this paper we computed t (P n 2 ,i),and obtain the polynomial D t (P n 2 ,x) = d t (P n 2 , i)x i n i=ϒ t (P n 2 ) which we call total domination polynomial of P n 2 , n ≥2 and obtain some properties of this polynomial.