Imran Allie

activity

20222025

collaborators

3 papers

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

Resistance, oddness and colouring defect of snarks

Imran Allie

Let $G$ be a bridgeless cubic graph. The \textit{resistance} of $G$ , denoted $r (G)$ , is the minimum number of edges which can be removed from $G$ in order to render 3-edge-colourab…

math.CO2022

3-critical subgraphs of snarks

Imran Allie

In this paper we further our understanding of the structure of class two cubic graphs, or snarks, as they are commonly known. We do this by investigating their 3-critical subgraphs…