Recurrence relations and splitting formulas for the domination polynomial

Tomer Kotek, James Preen, Frank Simon, Peter Tittmann, Martin Trinks

Published 2012-06-26, updated 2012-09-18Version 2

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.