Research · Luke Collins

My areas of interest in mathematical research are combinatorics, graph theory and number theory.

Publications

Two non-isomorphic graphs that share the same canonical double cover — Two graphs having the same canonical double cover

The Walks and CDCs of Graphs with the Same Main Eigenspace Luke Collins & Irene Sciriha Discussiones Mathematicae Graph Theory, 43(2) (2023)
DOI Journal
The Ternary Goldbach Conjecture Luke Collins Master’s Dissertation in Mathematics, University of Warwick (2020)
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On Walks and Canonical Double Coverings of Graphs with the Same Main Eigenspace Luke Collins Undergraduate Dissertation in Mathematics, University of Malta (2019)
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Synthesising Safety Runtime Enforcement Monitors for μHML Luke Collins Undergraduate Dissertation in Computer Science, University of Malta (2019)
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Two-graphs and NSSDs: An Algebraic Approach Luke Collins & Irene Sciriha Discrete Applied Mathematics, 266 (2018), 92–102
DOI Journal

Walks and CDCs

As an undergraduate, I did some research related to walks and an operation called the canonical double cover (CDC) of a graph. You can read more about this research here.