Graphs and Combinatorics

, Volume 30, Issue 3, pp 527–547

On the Roots of Domination Polynomials

Original Paper

DOI: 10.1007/s00373-013-1306-z

Cite this article as:
Brown, J.I. & Tufts, J. Graphs and Combinatorics (2014) 30: 527. doi:10.1007/s00373-013-1306-z

Abstract

The domination polynomial of a graph G of order n is the polynomial \({D(G, x) = \sum_{i=\gamma(G)}^{n} d(G, i)x^i}\) where d(G, i) is the number of dominating sets of G of size i, and γ(G) is the domination number of G. We investigate here domination roots, the roots of domination polynomials. We provide an explicit family of graphs for which the domination roots are in the right half-plane. We also determine the limiting curves for domination roots of complete bipartite graphs. Finally, we prove that the closure of the roots is the entire complex plane.

Keywords

Domination polynomialGraphDomination rootStableClosure

Mathematics Subject Classification (2000)

05C6905E15

Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada