On Pendant Domination Polynomial in the Corona of Some Graphs

Source abstract

A dominating set S in G is called a pendant dominating set if ⟨S⟩ contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number denoted by γpe(G). The pendant domination polynomial of G is denoted by Dpe(G, x) and is defined as Dpe(G, x) = Pn i=γpe(G) dpe(G, i)x i , where dpe(G, i)x i is the number of pendant dominating sets of size i. In this paper, we obtained the pendant domination number and pendant domination polynomial of the corona of some graphs, namely, Pm ◦ Kn, Cm ◦ Kn and Km ◦ Kn.