Some history of the development of graffiti

Abstract

Abstract. 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.

Graffiti.pc: A variant of graffiti

“…At its inception, it had the capability of generating about one hundred and thirty graph theoretical invariants, most of which were on degree and distance invariants of a graph, its complement graph and its second power graph 4 . However, Graffiti.pc's dalmatians subprogram very closely implements the principles of Fajtlowicz's dalmatian heuristic as described in the next section; a more detailed description is found in [4]. Overall, the most striking difference is Graffiti.pc's graphical user interface, since Graffiti is a Unix platform, menu and file driven program.…”

“…At this time, Graffiti.pc, unlike Graffiti, does not have an option for resuming the generation of conjectures 4. The second power of a graph G = (V, E), is the graph on vertex set V such that two vertices are adjacent if and only if the vertices are at distance at most two in the graph G 5.…”

Quantitative Graph Theory: A new branch of graph theory and network science

“…Conjecture engines [30,56] are tools that have been used to generate conjectures when proving statements on topological graph measures. They can be used to test the validity of inequalities involving topoological graph measures.…”

“…They can be used to test the validity of inequalities involving topoological graph measures. The tool Graffiti [30] is a prominent example and has been famous for generating conjectures involving the general and simple Randić index. A succesor thereof is GrInvIn [56] which is a freely available as Java-Application A shortcoming of GrInvIn is the quite weak conjecture engines which does not allow to use this tool to explore complex conjectures.…”

Variable neighborhood search for extremal graphs.17. Further conjectures and results about the index

“…The role of the computer in graph theory is rapidly increasing, see e.g. [10,14,15,16] for surveys and discussions. To the traditional tasks of invariant computation, graph drawing and graph enumeration by computer, several others have been added.…”