Generalizing works of D'Angeli and Donno, we describe, given an infinite sequence over the alphabet {0,…,r−1}, with r not divisible by 4, a sequence of pointed finite graphs. We study the pointed Gromov–Hausdorff limit graphs giving a description of isomorphism classes in terms of dihedral groups and we provide a description of the horofunction boundary, distinguishing between Busemann and non-Busemann points.
D'Angeli, D., Matucci, F., Perego, D., Rodaro, E. (2026). Horofunctions of infinite Sierpinski polygon graphs. DISCRETE MATHEMATICS, 349(8) [10.1016/j.disc.2026.115099].
Horofunctions of infinite Sierpinski polygon graphs
Matucci, F;
2026
Abstract
Generalizing works of D'Angeli and Donno, we describe, given an infinite sequence over the alphabet {0,…,r−1}, with r not divisible by 4, a sequence of pointed finite graphs. We study the pointed Gromov–Hausdorff limit graphs giving a description of isomorphism classes in terms of dihedral groups and we provide a description of the horofunction boundary, distinguishing between Busemann and non-Busemann points.
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