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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 of a graph from below by its equator , girth and minimum degree - 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 of a graph with diameter and maximum degree . This problem is well studied, and has been s…