P. Dankelmann

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20242026

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6 papers · 1 filter

math.CO2026

On fixing and distinguishing numbers of trees

Calum Buchanan, Peter Dankelmann, Isabel Harris +3

A graph $G$ is $D$ -distinguishable if there is a labeling of its vertices with $D$ labels such that the only automorphism of $G$ which preserves the labeling is the identity. The d…

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

Distance Sequences to bound the Harary Index and other Wiener-type Indices of a Graph

Peter Dankelmann

In this paper we obtain bounds on a very general class of distance-based topological indices of graphs, which includes the Wiener index, defined as the sum of the distances between…

math.CO2024

On the Edge-Connectivity of the Square of a Graph

Camino Balbuena, Peter Dankelmann

Let $G$ be a connected graph. The edge-connectivity of $G$ , denoted by $I^» (G)$ , is the minimum number of edges whose removal renders $G$ disconnected. Let $I^´ (G)$ be the minimum de…

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…