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math.CO2025
The Cycle Counts of Graphs
Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori +1
We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptio…
math.CO2025
Incidence Gain Graphs and Generalized Quadrangles
Ryan McCulloch
We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linea…
math.CO2024
Locally resolvable BIBDs and generalized quadrangles with ovoids
Ryan McCulloch
In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-tria…