On the real roots of domination polynomials

Authors

  • Jason Brown Dalhousie University
  • Iain Beaton Dalhousie University

DOI:

https://doi.org/10.11575/cdm.v16i3.72075

Abstract

A dominating set $S$ of a graph $G$ of order $n$ is a subset of the vertices of $G$ such that every vertex is either in $S$ or adjacent to a vertex of $S$. The domination polynomial is defined by $D(G,x) = \sum d_k x^k$ where $d_k$ is the number of dominating sets in $G$ with cardinality $k$. In this paper we show that the closure of the real roots of domination polynomials is $(-\infty,0]$.

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Published

2021-12-31

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Articles