Infectious power domination of hypergraphs

TL;DR

This paper introduces infectious power domination in hypergraphs, a new method combining domination and infection rules to optimize sensor placement in power networks, with theoretical bounds and analysis of hypergraph operations.

Contribution

It generalizes power domination to hypergraphs using an infection rule, providing bounds and analyzing effects of hypergraph operations, a novel approach in the field.

Findings

Provides bounds for infectious power domination

Analyzes impact of hypergraph operations

Compares with previous generalization by Chang and Roussel

Abstract

The power domination problem seeks to find the placement of the minimum number of sensors needed to monitor an electric power network. We generalize the power domination problem to hypergraphs using the infection rule from Bergen et al: given an initial set of observed vertices, $S_0$, a set $A\subseteq S_0$ may infect an edge $e$ if $A\subseteq e$ and for any unobserved vertex $v$, if $A\cup \{v\}$ is contained in an edge, then $v\in e$. We combine a domination step with this infection rule to create \emph{infectious power domination}. We compare this new parameter to the previous generalization by Chang and Roussel. We provide general bounds and determine the impact of some hypergraph operations.