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### On conjectures of Graffiti

Siemion Fajtlowicz
1988 Discrete Mathematics
For each false conjecture I had to inform Graffiti about a counterexample; Graffiti is capable of defining certain types of graphs and of performing some operations on graphs leading to more complex examples  ...  Perhaps some conjectures which Graffiti has already made are difficult to prove but in most of the cases one can clearly see a reason for making the conjecture.  ...  I would like to thank Robert Cottingham for writing for me a fast program deleting the text of one file from another. Note added in Proof.  ...

### On Conjectures of Graffiti [chapter]

Siemion Fajtlowicz
1988 Annals of Discrete Mathematics
For each false conjecture I had to inform Graffiti about a counterexample; Graffiti is capable of defining certain types of graphs and of performing some operations on graphs leading to more complex examples  ...  Perhaps some conjectures which Graffiti has already made are difficult to prove but in most of the cases one can clearly see a reason for making the conjecture.  ...  I would like to thank Robert Cottingham for writing for me a fast program deleting the text of one file from another. Note added in Proof.  ...

### On some conjectures of Graffiti

Béla Bollobás, Oliver Riordan
1998 Discrete Mathematics
We prove one of these conjectures, and disprove four.  ...  Returning to the property of k-colourability, in the original version of [5], DeLaVina and Fajtlowicz also listed several conjectures made by the conjecture making program Graffiti [8].  ...  Such graphs exist by theorems of Tutte [6] and Erdfs [7] The above result provides counterexamples to the third conjecture, for all values of r = max{c(v)} greater than one.  ...

### On the two conjectures of Graffiti

Xiao-Dong Zhang
2004 Linear Algebra and its Applications
Then the results are used to confirm two conjectures of Graffiti (WOW Conjectures 584 and 636) on the relationship between the Laplacian eigenvalues and the independence number of a graph.  ...  We study the Laplacian eigenvalues of trees on n vertices with independence number α and describe all extremal graphs that attain the maximal Laplacian spectral radius and algebraic connectivity.  ...  Conjecture 1.1 (WOW Conjecture 584).Let T be a tree of order n with independence number α. Then λ 1 < 2 + α. Conjecture 1.2 (WOW Conjecture 636).  ...

### On the two conjectures of Graffiti*1

X ZHANG
2004 Linear Algebra and its Applications
Then the results are used to confirm two conjectures of Graffiti (WOW Conjectures 584 and 636) on the relationship between the Laplacian eigenvalues and the independence number of a graph.  ...  We study the Laplacian eigenvalues of trees on n vertices with independence number α and describe all extremal graphs that attain the maximal Laplacian spectral radius and algebraic connectivity.  ...  Conjecture 1.1 (WOW Conjecture 584).Let T be a tree of order n with independence number α. Then λ 1 < 2 + α. Conjecture 1.2 (WOW Conjecture 636).  ...

### On some conjectures of Griggs and graffiti [chapter]

Ermelinda DeLaVina, Siemion Fajtlowicz, William Waller
2007 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
We prove a generalization of this conjecture made by the computer program Graffiti, and discuss other similar conjectures, including several generalizations of the theorem that the independence number  ...  We discuss a conjecture of J. R. Griggs relating the maximum number of leaves in a spanning tree of a simple, connected graph to the order and independence number of the graph.  ...  Acknowledgments: The authors wish to thank the referee for comments regarding the origin of Conjecture 1; and L. Lovasz for permission to quote his result regarding Conjecture 3.  ...

### A computational attack on the conjectures of Graffiti: New counterexamples and proofs

Tony L. Brewster, Michael J. Dinneen, Vance Faber
1995 Discrete Mathematics
Graffiti is a computer program that checks for relationships among certain graph invariants. It uses a database of graphs and has generated well over 700 conjectures.  ...  Having obtained a readily available computer tape of all the nonisomorphic graphs with 10 or fewer vertices, we have tested approximately 200 of the Graffiti conjectures and have found counterexamples  ...  A conjecture generating program, called Graffiti, was developed by Siemion Fajtlowicz in 1986 (see "Written on the Wall" [5] ).  ...

### Some history of the development of graffiti [chapter]

Ermelinda DeLaVina
2007 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
This paper provides some history of the development of the conjecturemaking computer program, Graffiti. In the process, its old and new heuristics are discussed and demonstrated.  ...  A note of gratitude is extended to Siemion Fajtlowicz for allowing the author access to all current and old code of the two versions of Graffiti.  ...  In addition, a note of thanks is extended to the anonymous referees of this paper for their helpful suggestions.  ...

### Program Accelerators and Automated Conjectures

Siemion Fajtlowicz
2013 Journal of Applied & Computational Mathematics
Since responses to conjectures, although highly subjective, are one of the simplest predictors of their potential, it should be noted that conjectures of Graffiti inspired results by many researchers including  ...  Before I had a chance to finish [4] , to refute the claim of Professor Simon on theoretical grounds, the "carbon" version of Graffiti conjectured, that the first eight observed fullerenes tend to minimize  ...

### Guessing at the Content of a Million Books

Patrick Juola
2017 Scholarly and Research Communication
The recent growth in digital scholarship has made literally millions of books available to readers. But the implications of this, paradoxically, are that reading becomes more difficult.  ...  This is particularly problematic in literary scholarship, where "reading" a text requires much more than simple content extraction, but may require identifying and explaining patterns of thought and expression  ...  The Graffiti program, in particular, researches graph theory through the generation and testing of conjectures.  ...

### Graffiti.pc: A variant of graffiti [chapter]

Ermelinda DeLaVina
2007 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
Graffiti.pc is a new conjecture-making program, whose design was influenced by the well-known conjecture making program, Graffiti.  ...  The subsequent sections describe the form of conjectures and educational applications of Graffiti.pc to undergraduate research in graph theory.  ...  This inequality is easily shown to be equivalent to α(G) ≤ 1 + ∆(G), which the student had also proven, as it was on a list of Graffiti.pc's conjectures.  ...

### On the notion of interestingness in automated mathematical discovery

SIMON COLTON, ALAN BUNDY, TOBY WALSH
2000 International Journal of Human-Computer Studies
We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery.  ...  We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics.  ...  We would also like to thank Susan Epstein for her comments explaining aspects of the GT program, JanŻytkow for his comments on the system by Bagai et al and Craig Larson for helping us understand the Graffiti  ...

### Spanning Trees with Many Leaves and Average Distance

Ermelinda DeLaViña, Bill Waller
2008 Electronic Journal of Combinatorics
These new lower bounds were conjectured by the program Graffiti.pc, a variant of the program Graffiti.  ...  If correct, this conjecture would generalize conjecture number 2 of Graffiti, which states that the average distance is not more than the independence number.  ...  This conjecture has been one of the most circulated of Graffiti's open conjectures (see [29] ).  ...

### Principles of human—computer collaboration for knowledge discovery in science

Raúl E. Valdés-Pérez
1999 Artificial Intelligence
Our candidate for a commonality, which focuses on human factors, can be used pragmatically to evaluate and compare the designs of discovery programs that are intended to be used as collaborators by scientists  ...  general--but weak--framework of heuristic search.  ...  Thanks to Siemion Fajtlowicz and Don Swanson for comments on the descriptions of the GRAFFITI and ARROWSMITH programs; any remaining inaccuracies are not their responsibility.  ...

### A survey of research in automated mathematical conjecture-making [chapter]

C. Larson
2007 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
A central and important idea underlying this program is the Principle of the Strongest Conjecture: make the strongest conjecture for which no counterexample is known.  ...  These two programs as well as other attempts to automate mathematical conjecture-making are surveyed-the success of a conjecture-making program, it is found, correlates strongly whether the program is  ...  Fajtlowicz's program was first described in his series of papers, "On Conjectures of Graffiti." The statements Graffiti has produced are largely novel.  ...
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