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4 papers · 2 filters
Progress towards the two-thirds conjecture on locating-total dominating sets
Dipayan Chakraborty, Florent Foucaud, Anni Hakanen +2
We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set of vertices of a graph is a locating-total dominating set if every vertex of $G…
Monitoring edge-geodetic sets in graphs
Subhadeep R. Dev, Sanjana Dey, Florent Foucaud +2
We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in…
On the unicyclic graphs having vertices that belong to all their (strong) metric bases
Anni Hakanen, Ville Junnila, Tero Laihonen +1
A metric basis in a graph is a smallest possible set of vertices of , with the property that any two vertices of are uniquely recognized by using a vector of distanc…
Revisiting and improving upper bounds for identifying codes
Florent Foucaud, Tuomo Lehtilä
An identifying code of a graph is a dominating set of such that any two distinct vertices of have distinct closed neighbourhoods within . These codes have been w…