5 citations · 5 across the 17 of their papers we have counts for
15 papers · 1 filter
A Systematic Approach to Crossing Numbers of Cartesian Products with Paths
Zayed Asiri, Ryan Burdett, Markus Chimani +3
Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the est…
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 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…