To investigate hyperbinary expansions of a nonnegative integer n, an edge-labeled directed graph A(n) has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple description of its structure and prove that if m, n are even numbers for which A(n) and A(m) are isomorphic as edge-labeled graphs, then m=n. From the structure of A(n) we also derive a formula related to Stern’s diatomic sequence, and in the same vein discuss some algorithms that recently appeared in the literature.
Isomorphisms of Graphs of Hyperbinary Expansions and Efficient Algorithms for Stern’s Diatomic Sequence
Alessandro De Paris
2026-01-01
Abstract
To investigate hyperbinary expansions of a nonnegative integer n, an edge-labeled directed graph A(n) has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple description of its structure and prove that if m, n are even numbers for which A(n) and A(m) are isomorphic as edge-labeled graphs, then m=n. From the structure of A(n) we also derive a formula related to Stern’s diatomic sequence, and in the same vein discuss some algorithms that recently appeared in the literature.File in questo prodotto:
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