5 citations · 5 across the 15 of their papers we have counts for
19 papers
Constructing Families of Cospectral Regular Graphs
Michael Haythorpe, Alex Newcombe
A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite fami…
The maximum crossing number of
Michael Haythorpe, Alex Newcombe
We determine that the maximum crossing number of is 78, which closes the previously best known range of between 68 and 80. The proof uses several techniques which…
An improved binary programming formulation for the secure domination problem
Ryan Burdett, Michael Haythorpe
The secure domination problem, a variation of the domination problem with some important real-world applications, is considered. Very few algorithmic attempts to solve this problem…
On the Crossing Number of the Cartesian Product of a Sunlet Graph and a Star Graph
Michael Haythorpe, Alex Newcombe
The exact crossing number is only known for a small number of families of graphs. Many of the families for which crossing numbers have been determined correspond to cartesian produ…
A Note on Using the Resistance-Distance Matrix to solve Hamiltonian Cycle Problem
Vladimir Ejov, Jerzy A Filar, Michael Haythorpe +2
An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying gr…
A Linearly-growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem
Michael Haythorpe, Jerzy Filar
We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it…