Optimal Domination Polynomials

I. Beaton; J. I. Brown; D. Cox

Optimal Domination Polynomials

Combinatorics 2019-04-15 v1

Authors: I. Beaton , J. I. Brown , D. Cox

Abstract

Let $G$ be a graph on $n$ vertices and $m$ edges and $D(G,x)$ the domination polynomial of $G$ . In this paper we completely characterize the values of $n$ and $m$ for which optimal graphs exist for domination polynomials. We also show that there does not always exist least optimal graphs for the domination polynomial. Applications to network reliability are highlighted.

Keywords

domination in graphs graph theory graph pebbling

Cite

@article{arxiv.1904.06267,
  title  = {Optimal Domination Polynomials},
  author = {I. Beaton and J. I. Brown and D. Cox},
  journal= {arXiv preprint arXiv:1904.06267},
  year   = {2019}
}

Comments

13 pages

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