OEIS A00000: Minimal Triangle Graphs

We explore the counting of nonisomorphic minimal triangle graphs on n vertices — graphs in which every triangle is indispensable to the structure. The sequence begins 1, 1, 2, 4, 9, 19, and traces back to Bowen’s 1967 work, with later work (2014, Discrete Mathematics) on three minimal triangle-free graphs showing the P4 as a key building block and providing a precise counting formula. These ideas illuminate how specific local structures influence global network properties and robustness.

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