12 citations · 13 across the 6 of their papers we have counts for
6 papers
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…
Minimal Regular graphs with every edge in a triangle
James Preen
Considering regular graphs with every edge in a triangle we prove lower bounds for the number of triangles in such graphs. For r-regular graphs with r <= 5 we exhibit families of g…
Bivariate Domination Polynomial
James Preen, Alexander Murray
We introduce a new bivariate polynomial which contains the standard domination polynomial of the graph i…
Domination Polynomials of Graph Products
Tomer Kotek, James Preen, Peter Tittmann
The domination polynomials of binary graph operations, aside from union, join and corona, have not been widely studied. We compute and prove recurrence formulae and properties of t…
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…