Graphs and Combinatorics

, Volume 29, Issue 5, pp 1175–1181

The Domination Polynomial of a Graph at −1

Original Paper

DOI: 10.1007/s00373-012-1211-x

Cite this article as:
Alikhani, S. Graphs and Combinatorics (2013) 29: 1175. doi:10.1007/s00373-012-1211-x


Let G be a simple graph. The domination polynomial of a graph G of order n is the polynomial \({D(G,x)=\sum_{i=0}^{n} d(G,i) x^{i}}\) , where d(G, i) is the number of dominating sets of G of size i. In this article we investigate the domination polynomial at −1. We give a construction showing that for each odd number n there is a connected graph G with D(G, −1) = n.


Domination polynomialValue

Mathematics Subject Classification (2000)

Primary 05C60

Copyright information

© Springer 2012

Authors and Affiliations

  1. 1.Department of MathematicsYazd UniversityYazdIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran