Sonwabile Mafunda

activity

20202025

most citedProximity, remoteness and maximum degree in graphs

2 citations · 5 across the 11 of their papers we have counts for

collaborators

11 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 $κ$ . It was shown by A…

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…

math.CO2024

Remoteness of graphs with given size and connectivity constraints

Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu

Let $G$ be a finite, simple 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 remotene…

math.CO2024

Paint cost spectrum of perfect $k$ -ary trees

Sonwabile Mafunda, Jonathan L. Merzel, K. E. Perry +1

We determine the paint cost spectrum for perfect $k$ -ary trees. A coloring of the vertices of a graph $G$ with $d$ colors is said to be \emph{ $d$ -distinguishing} if only the trivia…

math.CO2022★ 2 cited

Proximity, remoteness and maximum degree in graphs

Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu

The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$ . The proximity $π (G)$ and the remoteness…

math.CO2021★ 1 cited

On the difference between proximity and other distance parameters in triangle-free graphs and $C_{4}$ -free graphs

Peter Dankelmann, Sonwabile Mafunda

The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$ . The proximity $π (G)$ and the remoteness…

math.CO2020★ 1 cited

An Extremal Problem on Rainbow Spanning Trees in Graphs

Matthew DeVilbiss, Bradley Fain, Amber Holmes +3

A spanning tree of an edge-colored graph is rainbow provided that each of its edges receives a distinct color. In this paper we consider the natural extremal problem of maximizing…

math.CO2020

Proximity and remoteness in triangle-free and C_4-free graphs in terms of order and minimum degree

Peter Dankelmann, Elizabeth Jonck, Sonwabile Mafunda

Let $G$ be a finite, 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 remoteness $ρ(G…

math.CO2020★ 1 cited

Proximity and Remoteness in Directed and Undirected Graphs

Jiangdong Ai, Stefanie Gerke, Gregory Gutin +1

Let $D$ be a strongly connected digraph. The average distance $σ ˉ (v)$ of a vertex $v$ of $D$ is the arithmetic mean of the distances from $v$ to all other vertices of $D$ . The r…

Size of bipartite graphs with given diameter and connectivity constraints

A Note on Distance-Fall Colorings

On Proximity and other Distance Parameters in Planar Graphs

Proximity and Radius in Outerplanar Graphs with Bounded Faces

Remoteness of graphs with given size and connectivity constraints

Paint cost spectrum of perfect k-ary trees

Proximity, remoteness and maximum degree in graphs

On the difference between proximity and other distance parameters in triangle-free graphs and C4​-free graphs

An Extremal Problem on Rainbow Spanning Trees in Graphs

Proximity and remoteness in triangle-free and C_4-free graphs in terms of order and minimum degree

Proximity and Remoteness in Directed and Undirected Graphs

Paint cost spectrum of perfect $k$ -ary trees

On the difference between proximity and other distance parameters in triangle-free graphs and $C_{4}$ -free graphs