Some families of graphs with no nonzero real domination roots - Somayeh Jahari; Saeid Alikhani (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2018)
Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G, x) = ∑ni = γ(G)d(G, i)xi, where d(G, i) is the number of dominating sets of G of size i and γ(G) is the domination number of G. A root of D(G, x) is called a domination root of G. Obviously, 0 is a domination root of every graph G with multiplicity γ(G). In the study of the domination roots of graphs, this naturally raises the question: Which graphs have no nonzero real domination roots? In this paper we present some families of graphs whose have this property.