Some families of graphs with no nonzero real domination roots

• Published in: Electronic journal of graph theory and applications Vol. 6; no. 1; pp. 17 - 28
• Main Authors: Jahari, Somayeh, Alikhani, Saeid
• Format: Journal Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 01.01.2018
• Subjects: domination polynomial, domination root, friendship, complex root
• ISSN: 2338-2287; 2338-2287
• DOI: 10.5614/ejgta.2018.6.1.2

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.