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math.CO2021
Quintic graphs with every edge in a triangle
James Preen
We characterise the quintic (i.e. 5-regular) multigraphs with the property that every edge lies in a triangle. Such a graph is either from a set of small graphs or is formed by add…
math.CO2017
Bivariate Domination Polynomial
James Preen, Alexander Murray
We introduce a new bivariate polynomial which contains the standard domination polynomial of the graph i…
math.CO2012
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…