Average independence polynomials
نویسندگان
چکیده
The independence polynomial of a graph G is the function i(G, x) = ∑k 0 ikx , where ik is the number of independent sets of vertices in G of cardinality k. We investigate here the average independence polynomial, where the average is taken over all independence polynomials of (labeled) graphs of order n. We prove that while almost every independence polynomial has a nonreal root, the average independence polynomials always have all real, simple roots. © 2004 Elsevier Inc. All rights reserved.
منابع مشابه
On the Stability of Independence Polynomials
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We investigate the stability of such polynomials, that is, conditions under which the independence roots lie in the left half-plane. We use results from complex analysis to determine graph operations that result in a stable or nonstable...
متن کاملApproximating independence polynomials of claw-free graphs
Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...
متن کاملUnimodality of the independence polynomials of non-regular caterpillars
The independence polynomial I(G, x) of a graph G is the polynomial in variable x in which the coefficient an on x n gives the number of independent subsets S ⊆ V (G) of vertices of G such that |S| = n. I(G, x) is unimodal if there is an index μ such that a0 ≤ a1 ≤ · · · ≤ aμ−1 ≤ aμ ≥ aμ+1 ≥ · · · ≥ ad−1 ≥ ad. While the independence polynomials of many families of graphs with highly regular stru...
متن کاملOn the Location of Roots of Independence Polynomials
The independence polynomial of a graph G is the function i(G, x) = ∑k≥0 ik xk , where ik is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (−∞, 0], while complex roots are dense in C, even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are...
متن کاملOn the independence polynomials of path-like graphs
We investigate the independence polynomials of members of various infinite families of path-like graphs, showing that the coefficient sequences of such polynomials are logarithmically concave.
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:
- J. Comb. Theory, Ser. B
دوره 93 شماره
صفحات -
تاریخ انتشار 2005