Lewis Stanton

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20222024

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math.CO2022

Graphs with equal girth and circumference

Lewis Stanton, Jeffrey Thompson

We characterise the form of all simple, finite graphs for which the girth of the graph is equal to the circumference of the graph. We apply this to prove a bound on the number of e…

math.CO2022

Structure of a Maximal Total Independent Set

Lewis Stanton

Let $G$ be a simple, connected and finite graph with order $n$ . Denote the independence number, edge independence number and total independence number by $α (G), α^{'} (G)$ and $α " (G)$ …