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GraphData: New Developments and Research Applications

1,025 views · Published 3 February 2014 · 12:51 · Indexed 14 November 2026

Channel: Wolfram · 2014 · Education

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GraphData is an extensive curated database of simple graphs and their properties available in Mathematica as a built-in data paclet and in Wolfram|Alpha via natural language queries. GraphData was first introduced in Mathematica Version 6, and the number of graphs, property count, and fraction of properties filled in continues to grow with each subsequent release of Mathematica. In Version 10 (as of this writing), GraphData will contain 7844 graphs, 398 properties, and 192 classes.

In this talk, Eric Weisstein will discuss the current state of GraphData together with some plans for the future, and Stan Wagon will discuss GraphData-inspired and largely Mathematica-based graph theoretic computations which not only have substantially filled in properties for many graphs, but also led to some interesting mathematical conjectures.

New algorithms led to a 100% success rate in determining several properties for graphs in GraphData, such as the existence of a Hamiltonian decomposition, and 99% success for some more difficult ones, such as chromatic number. This work leads to interesting new conjectures, the most prominent of which are: (1) with one exception, every Hamiltonian vertex-transitive graph has a Hamiltonian decomposition and (2) with one exception, every Hamiltonian vertex-transitive graph is Hamilton-connected (or Hamilton-laceable). These conjectures have been verified on over 100,000 vertex-transitive graphs. Computations can point the way to new theorems as well, such as a characterization of bishop graphs that are Hamiltonian, knight graphs that are Hamilton-connected, and Mycielski graphs that are Hamilton-connected.

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