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- The University of AdelaideAU19 papers
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9 papers · 1 filter
The gerrymander sequence, or A348456
Anthony J Guttmann, Iwan Jensen
Recently Kauers, Koutschan and Spahn announced a significant increase in the length of the so-called {\em gerrymander sequence}, given as A348456 in the OEIS, extending the sequenc…
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…
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…
Constructing Arbitrarily Large Graphs with a Specified Number of Hamiltonian Cycles
Michael Haythorpe
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing vertices and Hamiltonian cycles for any choice of integer…
A New Heuristic for Detecting Non-Hamiltonicity in Cubic Graphs
Jerzy A Filar, Michael Haythorpe, Serguei Rossomakhine
We analyse a polyhedron which contains the convex hull of all Hamiltonian cycles of a given undirected connected cubic graph. Our constructed polyhedron is defined by polynomially-…