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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Saeid Alikhani
Department of Mathematics‎, ‎Yazd University‎, ‎89195-741‎, ‎Yazd‎, ‎Iran
Electrical & Electronics Engineering

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Some families of graphs with no nonzero real domination roots Somayeh Jahari; Saeid Alikhani
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.1.2

Abstract

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.
Co-Authors Somayeh Jahari