The AutoGraphiX system (AGX 1 and AGX 2) for interactive, and for several functions automated, graph theory, discovers conjectures of algebraic or structura...

A graph invariant is a function of a graph <i>G</i> which does not depend on labeling of <i>G</i>’s vertices or edges. An algebraic expression of one or sev...

The multidimensional scaling (MDS) aims at finding coordinates for a set of <i>n</i> objects in a (low) <i>q</i> dimensional space that best fits dissimilar...

We consider the problem of separating two sets of points in an Euclidean space with a hyperplane that minimizes the sum of <i>L_p</i>-norm distanc...

<i>L</i>₁ norm discrimination consists in finding the hyperplane that minimizes the sum of <i>L</i>₁ norm distances between the hyperp...

A survey is made of the AutoGraphiX (AGX) research program for computer as- sisted and, for some functions, automated graph theory.

The AutoGraphiX (AGX) system for computer assisted or, for some of its functions, fully automated graph theory was developed at GERAD, Montreal since 1997. ...

In this paper, we present tools to help understanding the dynamics of cognitive processes involved in handwriting and in text composition. Three computer sy...

Conjectures in graph theory have multiple forms and involve graph invariants, graph classes, subgraphs, minors and other concepts in premisses and/or conclu...

Let <i>G</i> be a simple graph on <i>n</i> vertices with the eigenvalues (of an adjacency matrix) &lambda;₁ &ge; &lambda;₂ &ge; ... &g...

After a short historic review, we briefly describe a new algorithm for constructive enumeration of polyhex and fusene hydrocarbons. In this process our alg...

The AutoGraphiX (AGX) system determines classes of extremal or near extremal graphs with a Variable Neighborhood Search heuristic. From these, conjectures m...

Let <i>G</i> be a graph and <i>d_v</i> the degree (= number of first neighbors) of its vertex <i>v</i>. The connectivity index of <i>G</i> is <img...

In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non is...

Graffiti's conjecture 105 states that for any tree the range of transmissions of distance is greater than or equal to the range of degrees. After using the ...

On the basis of a variable-neighbourhood search with the AutoGraphiX software, it is conjectured that for even numbers of atoms the fully conjugated acycli...

The distance matrix of a chemical graph can be computed in quadratic time, and from it can be obtained the distance level patterns (DLP), Wiener, Szeged and...

In the set of bicolored trees with given numbers of black and of white vertices we describe those for which the largest eigenvalue is extremal (maximal or m...

The definition of a fullerene as a cubic polyhedron made up entirely of pentagons and hexagons is compatible with a huge variety of isomeric forms for struc...

Fusenes are simply connected, geometrically planar or non-planar polyhexes. Enumeration of such systems with up to 20 hexagons, <i>i.e.,</i> a set 4000 tim...