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4 papers · 2 filters
Subset-Sum Representations of Domination Polynomials
Tomer Kotek, James Preen, Peter Tittmann
The domination polynomial D(G,x) is the ordinary generating function for the dominating sets of an undirected graph G=(V,E) with respect to their cardinality. We consider in this p…
Recurrence relations and splitting formulas for the domination polynomial
Tomer Kotek, James Preen, Frank Simon +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 r…
Proving properties of the edge elimination polynomial using equivalent graph polynomials
Martin Trinks
Averbouch, Godlin and Makowsky define the edge elimination polynomial of a graph by a recurrence relation with respect to the deletion, contraction and extraction of an edge. It ge…
Closed-form expansions for the bivariate chromatic polynomial of paths and cycles
Klaus Dohmen
We establish closed-form expansions for the number of colorings of a path or cycle on n vertices with colors from 1,...,x such that adjacent vertices are colored differently or wit…