189 citations · 219 across the 9 of their papers we have counts for
7 papers · 1 filter
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…
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…