Recurrence relations and splitting formulas for the domination polynomial
Combinatorics
2013-04-26 v2
Abstract
The domination polynomial D(G,x) of a graph G is the generating function of its dominating sets. We prove that D(G,x) satisfies a wide range of reduction formulas. We show linear recurrence relations for D(G,x) for arbitrary graphs and for various special cases. We give splitting formulas for D(G,x) based on articulation vertices, and more generally, on splitting sets of vertices.
Cite
@article{arxiv.1206.5926,
title = {Recurrence relations and splitting formulas for the domination polynomial},
author = {Tomer Kotek and James Preen and Frank Simon and Peter Tittmann and Martin Trinks},
journal= {arXiv preprint arXiv:1206.5926},
year = {2013}
}