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This work is in two independent parts, both about graph theory. A graph is a set of points called vertices, which can be close (neighbours) or not. In the first part, we study how to make graphs “irregular”, that is how to modify a graph so that two nodes that are close to each other can be distinguished by how many neighbours they have. In the second part, we study graphs that model networks, which are monitored for failure in connections. The problem consists in finding a monitoring edge-geodetic set, that is, a smallest set of nodes in the network, called probes, such that if a connexion fail, the latency of a communication between two probes changes. In terms of graphs, this means that if an edge is deleted, then the distance between two probes changes.
 

Amphi LaBRI