Final title: "More on domination polynomial and domination root" Previous title: "Graphs with domination roots in the right half-plane"

2013/05/16 by ‎Saeid Alikhani, Saeid Alikhani, Alikhani, Saeid +2
Computer Science · Mathematics · #05C60 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO #msc:05C60

paper · pdf · doi:10.48550/arxiv.1305.3734

18 Pages, 6 Figures. To appear in Ars Combin

openalex publication_date 2013/05/16 · arxiv created 2014/02/28 · arxiv updated 2014/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x) =∑ d(G, i)xⁱ, where d(G,i) is the number of dominating sets of G of size i. Every root of D(G,x) is called the domination root of G. It is clear that (0,∞) is zero free interval for domination polynomial of a graph. It is interesting to investigate graphs which have complex domination roots with positive real parts. In this paper, we first investigate complexity of the domination polynomial at specific points. Then we present and investigate some families of graphs whose complex domination roots have positive real part.

Citations

• Acyclic orientations of graphs

Related

• Some new results on domination roots of a graph
• An atlas of domination polynomials of graphs of order at most six
• Some families of graphs with no nonzero real domination roots
• Some new results on the total domination polynomial of a graph
• On the Real Roots of Domination Polynomials