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Updated: Mar 23, 2026

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Novel Sequence Discovery by Subtractive Genomics
Published on: January 25, 2019
9.2K
Integer sequence discovery from small graphs
Summary
Researchers enumerated finite simple connected graphs and computed graph invariants, adding 141 new integer sequences to the Online Encyclopedia of Integer Sequences (OEIS). This work provides an open-source framework for graph analysis and visualization.
Area of Science:
- Discrete Mathematics
- Graph Theory
- Computational Mathematics
Background:
- Enumeration of graph structures is fundamental in discrete mathematics.
- Graph invariants are crucial for classifying and understanding graph properties.
- The Online Encyclopedia of Integer Sequences (OEIS) serves as a repository for number sequences derived from mathematical objects.
Purpose of the Study:
- To exhaustively enumerate all simple, connected graphs of finite order.
- To compute a selection of graph invariants for the enumerated graphs.
- To identify and contribute new integer sequences to the OEIS.
Main Methods:
- Systematic enumeration of all simple, connected graphs.
- Computation of selected graph invariants for each graph.
- Generation of integer sequences from computed invariants.
- Comparison of generated sequences against the OEIS.
- Development of an open-source framework for graph analysis and visualization.
Main Results:
- Exhaustive enumeration of finite simple connected graphs completed.
- 141 new integer sequences added to the OEIS.
- Six existing OEIS sequences were extended.
- Programmatic suggestions for relationships among graph invariants were generated.
- A method for visualizing graph sequences based on criteria was demonstrated.
Conclusions:
- The study successfully expanded the OEIS with novel graph-derived sequences.
- The developed open-source framework facilitates further research in graph theory and invariant analysis.
- The graph database is designed for extensibility to include additional invariants.
- Programmatic identification of invariant relationships offers new avenues for graph theory research.
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