作者
Saieed Akbari, Saeid Alikhani, Yee-hock Peng
发表日期
2010/10/1
期刊
European journal of combinatorics
卷号
31
期号
7
页码范围
1714-1724
出版商
Academic Press
简介
Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=∑i=1nd(G,i)xi, where d(G,i) is the number of dominating sets of G of size i. A root of D(G,x) is called a domination root of G. We denote the set of distinct domination roots by Z(D(G,x)). Two graphs G and H are said to be D-equivalent, written as G∼H, if D(G,x)=D(H,x). The D-equivalence class of G is [G]={H:H∼G}. A graph G is said to be D-unique if [G]={G}. In this paper, we show that if a graph G has two distinct domination roots, then Z(D(G,x))={−2,0}. Also, if G is a graph with no pendant vertex and has three distinct domination roots, then Z(D(G,x))⊆{0,−2±2i,−3±3i2}. Also, we study the D-equivalence classes of some certain graphs. It is shown that if n≡0,2(mod3), then Cn is D-unique, and if n≡0(mod3), then [Pn] consists of exactly two graphs.
学术搜索中的文章
S Akbari, S Alikhani, Y Peng - European journal of combinatorics, 2010