Sonwabile Mafunda

collaborators

4 papers

math.CO2025

Size of bipartite graphs with given diameter and connectivity constraints

Sonwabile Mafunda

In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter $d$ , and connectivity $I^º$ . It was shown by…

math.CO2025

A Note on Distance-Fall Colorings

Wayne Goddard, Sonwabile Mafunda

We say a proper coloring of a graph is distance- $k$ fall if every vertex is within distance $k$ of at least one vertex of every color. We show that if $G$ is a connected graph of o…

math.CO2025

On Proximity and other Distance Parameters in Planar Graphs

Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu

Let $G$ be a connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$ . The proximity and remotenes…

math.CO2025

Proximity and Radius in Outerplanar Graphs with Bounded Faces

Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu

Let $G$ be a finite, connected graph and $v$ a vertex of $G$ . The average distance and the eccentricity of $v$ in $G$ are defined as the arithmetic mean and the maximum, respective…