• Corpus ID: 238259890

Unimodality and monotonic portions of certain domination polynomials

@inproceedings{Burcroff2021UnimodalityAM,
  title={Unimodality and monotonic portions of certain domination polynomials},
  author={Amanda Burcroff and Grace O'Brien},
  year={2021}
}
Given a simple graph G on n vertices, a subset of vertices U ⊆ V (G) is dominating if every vertex of V (G) is either in U or adjacent to a vertex of U . The domination polynomial of G is the generating function whose coefficients are the number of dominating sets of a given size. We show that the domination polynomial is unimodal, i.e., the coefficients are nondecreasing and then non-increasing, for several well-known families of graphs. In particular, we prove unimodality for spider graphs… 
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