189 citations · 219 across the 9 of their papers we have counts for
10 papers
Complete polyhedral description of chemical graphs of maximum degree at most 3
Valentin Dusollier, Sébastien Bonte, Gauvain Devillez +3
Chemical graphs are simple undirected connected graphs, where vertices represent atoms in a molecule and edges represent chemical bonds. A degree-based topological index is a molec…
Minimum Eccentric Connectivity Index for Graphs with Fixed Order and Fixed Number of Pending Vertices
Gauvain Devillez, Alain Hertz, Hadrien Mélot +1
The eccentric connectivity index of a connected graph is the sum over all vertices of the product , where is the degree of in and $e_{…
Maximum Eccentric Connectivity Index for Graphs with Given Diameter
Pierre Hauweele, Alain Hertz, Hadrien Mélot +2
The eccentricity of a vertex in a graph is the maximum distance between and any other vertex of . The diameter of a graph is the maximum eccentricity of a vertex…
PHOEG Helps Obtaining Extremal Graphs
Gauvain Devillez, Pierre Hauweele, Hadrien Mélot
Extremal Graph Theory aims to determine bounds for graph invariants as well as the graphs attaining those bounds. We are currently developping PHOEG, an ecosystem of tools designed…
On price of symmetrisation
Absil Romain, Hadrien Mélot
We introduce the price of symmetrisation, a concept that aims to compare fundamental differences (gap and quotient) between values of a given graph invariant for digraphs and the v…
Digenes: genetic algorithms to discover conjectures about directed and undirected graphs
Romain Absil, Hadrien Mélot
We present Digenes, a new discovery system that aims to help researchers in graph theory. While its main task is to find extremal graphs for a given (function of) invariants, it al…
House of Graphs: a database of interesting graphs
Gunnar Brinkmann, Kris Coolsaet, Jan Goedgebeur +1
In this note we present House of Graphs (http://hog.grinvin.org) which is a new database of graphs. The key principle is to have a searchable database and offer -- next to complete…
Trees with Given Stability Number and Minimum Number of Stable Sets
Véronique Bruyère, Gwenaël Joret, Hadrien Mélot
We study the structure of trees minimizing their number of stable sets for given order and stability number . Our main result is that the edges of a non-trivial extremal tre…
Fibonacci Index and Stability Number of Graphs: a Polyhedral Study
Véronique Bruyère, Hadrien Mélot
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight u…
Turán Graphs, Stability Number, and Fibonacci Index
Véronique Bruyère, Hadrien Mélot
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight u…