Joshua Connor graduated high school in 2012, after taking a year off from studying he decided to enrol in open foundation at the University of Newcastle in order to improve his mathematical skills before applying for a bachelor’s degree in science. There he found a deep curiosity about maths and has loved it ever since. Midway through second year (of a combined Maths and Science degree) he decided that he would perhaps like to make a career out of maths and when the University released their summer research options he applied for one in the field of Graph Theory. Joshua took graph theory in first year and found its simplistic looking, yet non-trivial nature quite intriguing.
Other areas of interest to Josh are differential equations, algebra, and number theory. Although yet to take the latter as an undergraduate, the thought of primes, their fundamental nature to mathematics and the mystery that surrounds them is extremely exciting. Beyond the vacation research project, Joshua will continue to finish his degree and apply for honours if the opportunity arises. Joshua also tutors maths to high school students, and forces his sister to study maths under his watchful eye.
Areas that he would like to have had a contribution in by the end of his career are pure mathematics, and mathematical education. He believes that if everyone could think a bit more like a mathematician the world would move along much faster.
Cycle Spectrum for Honeycomb Toroidal Graphs
To study Honeycomb Toroidal Graphs (HTG) of girth 4 and characterise their properties. This includes finding a set of cycle lengths that either permeate through all subsequent graphs and/or finding a set of cycle lengths that are achievable by any particular HTG. Finally once these are achieved, to find a constant such that all HTG have all even cycle lengths of said particular constant throughout the graph.