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Note on the Smallest Root of the Independence Polynomial

Published online by Cambridge University Press:  18 July 2012

PÉTER CSIKVÁRI
PÉTER CSIKVÁRI*
Affiliation:
Department of Computer Science, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary and Alfréd Rényi Institute of Mathematics, H-1053 Budapest, Reáltanoda u. 13-15, Hungary (e-mail: csiki@cs.elte.hu)
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Abstract

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 I(G,x)=∑k=0n(−1)kik(G)xk. In this paper we give a new proof of the fact that the root of I(G,x) having the smallest modulus is unique and is real.

Keywords

Primary 05C31
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 1 , January 2013 , pp. 1 - 8
Copyright
Copyright © Cambridge University Press 2012

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