# Complexity of Edge Monitoring on Some Graph Classes

1 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : In this paper, we study the complexity of the edge monitoring problem. A vertex $v$ monitors an edge $e$ if both extremities together with $v$ form a triangle in the graph. Given a graph $G=(V,E)$ and a weight function on edges $c$ where $c(e)$ is the number of monitors that needs the edge $e$, the problem is to seek a minimum subset of monitors $S$ such that every edge $e$ in the graph is monitored by at least $c(e)$ vertices in $S$. In this paper, we study the edge monitoring problem on several graph classes such as complete graphs, block graphs, cographs, split graphs, interval graphs and planar graphs. We also generalize the problem by adding weights on vertices.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-02167603
Submitted on : Thursday, June 27, 2019 - 10:42:42 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:52 PM

### Identifiers

• HAL Id : hal-02167603, version 1
• ARXIV : 1710.02013

### Citation

Guillaume Bagan, Fairouz Beggas, Mohammed Haddad, Hamamache Kheddouci. Complexity of Edge Monitoring on Some Graph Classes. 2019. ⟨hal-02167603⟩

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