Note on the Smallest Root of the Independence Polynomial
نویسنده
چکیده
One can define the independence polynomial of a graph G as follows. Let ik(G) denote the number of independent sets of size k of G, where i0(G) = 1. Then the independence polynomial of G is
منابع مشابه
On the Roots of Hosoya Polynomial of a Graph
Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...
متن کاملOn the roots of independence polynomials of almost all very well-covered graphs
If sk denotes the number of stable sets of cardinality k in graph G, and α(G) is the size of a maximum stable set, then I(G;x) = α(G) ∑ k=0 skx k is the independence polynomial of G (Gutman and Harary, 1983). A graph G is very well-covered (Favaron, 1982) if it has no isolated vertices, its order equals 2α(G) and it is well-covered (i.e., all its maximal independent sets are of the same size, M...
متن کاملNote on Some Elementary Properties of Polynomials
(4) cf ^ 2(1 d) >\ Equality holds only for f(x) = 1— x, a= — (1 —d). Suppose there exists a polynomial of degree n>2 satisfying (1) with Cf ̂ 2 ( 1 — d)\ then we will prove that there exists a polynomial of degree n — 1 with Cf >2(1 —d); and this proves (4) since it is easy to prove that (4) is satisfied for polynomials of second degree, that is, for l -# 2 . Denote the roots off(x) by Xi = — 1,...
متن کاملSome results on the polynomial numerical hulls of matrices
In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.
متن کامل?-Independent and Dissociate Sets on Compact Commutative Strong Hypergroups
In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 22 شماره
صفحات -
تاریخ انتشار 2013