Brandon Du Preez

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20222025

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6 papers · 1 filter

math.CO2025

Bounds on the propagation radius in power domination

Imran Allie, Brandon du Preez, Dean Reagon +1

Let $G$ be a graph and let $S \subseteq V (G)$ . It is said that $S$ \textit{dominates} $N [S]$ . We say that $S$ \textit{monitors} vertices of $G$ as follows. Initially, all dominated…

math.CO2024

Isometric Cycles and a Generalization of Moore Graphs

Brandon Du Preez

The equator of a graph is the length of a longest isometric cycle. We bound the order $n$ of a graph from below by its equator $q$ , girth $g$ and minimum degree $δ$ - and show that…

math.CO2024

Maximal planar graphs that embed as centers

Brandon Du Preez

A maximal planar graph is a graph which can be embedded in the plane such that every face of the graph is a triangle. The center of a graph is the subgraph induced by the vertices…

math.CO2024

The degree-diameter problem for plane graphs with pentagonal faces

Brandon Du Preez

The degree-diameter problem consists of finding the maximum number of vertices $n$ of a graph with diameter $d$ and maximum degree $Δ$ . This problem is well studied, and has been s…

math.CO2023

Disconnected cuts in 4-connected planar graphs

Brandon Du Preez

Let $G = (V, E)$ be a connected graph. A subset $S \subset V$ is a cut of $G$ if $G - S$ is disconnected. A near triangulation is a 2-connected plane graph that has at most one face that…

math.CO2022

Toughness of recursively partitionable graphs

Calum Buchanan, Brandon Du Preez, K. E. Perry +1

A simple graph $G = (V, E)$ on $n$ vertices is said to be recursively partitionable (RP) if $G ≃ K_{1}$ , or if $G$ is connected and satisfies the following recursive property: for…