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arXiv · 2512.14030

A Formal Analogue of Euler's Formula for Infinite Planar Regular Graphs

Piotr Jędrzejewicz·Mikołaj Marciniak
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Abstract

We present a formal version of the numbers of vertices, edges, and faces for infinite planar regular triangular meshes of degree r>6. These numbers are defined via Euler summation of sequences obtained from iterated expansions of a convex combinatorial disk. We prove that these formal quantities satisfy the classical Euler formula, providing a combinatorial analogue of Euler's formula for infinite planar graphs.

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Piotr Jędrzejewicz, Mikołaj Marciniak. 2025-12-16. A Formal Analogue of Euler's Formula for Infinite Planar Regular Graphs. https://arxiv.org/abs/2512.14030

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