Construction numbers: How to build a graph?

02/25/2023

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by   Paul C. Kainen, et al.

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We count the number of ways to build paths, stars, cycles, and complete graphs as a sequence of vertices and edges, where each edge follows both of its endpoints. The problem was considered 50 years ago by Stanley but the explicit sequences corresponding to graph families seem to have been little studied. A cost-based variant is introduced and applications are considered.