20 citations · 65 across the 20 of their papers we have counts for
35 papers
Generalising the achromatic number to Zaslavsky's colourings of signed graphs
Julien Bensmail, François Dross, Nacim Oijid +1
The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of the graph chromatic th…
A proof of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{ó}w in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we…
On a List Variant of the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with so that no two adjacent vertices are incident to the same sum of labels. In the last decades…
On the Broadcast Independence Number of Circulant Graphs
Abdelamin Laouar, Isma Bouchemakh, Eric Sopena
An independent broadcast on a graph is a function such that for every vertex , where $\operat…
(α, β)-Modules in Graphs
Michel Habib, Lalla Mouatadid, Eric Sopena +1
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a singl…
On the signed chromatic number of some classes of graphs
Julien Bensmail, Sandip Das, Soumen Nandi +3
A signed graph is a graph along with a function . A closed walk of a signed graph is positive (resp., negative) if it has an even (resp., odd) num…