Scholarlink

<p>To investigate hyperbinary expansions of a nonnegative integer&#xa0;<i>n</i>, an edge-labeled directed graph <i>A</i>(<i>n</i>) 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 <i>m</i>,&#xa0;<i>n</i> are even numbers for which <i>A</i>(<i>n</i>) and <i>A</i>(<i>m</i>) are isomorphic as edge-labeled graphs, then <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(m=n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>=</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>. From the structure of <i>A</i>(<i>n</i>) 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Isomorphisms of Graphs of Hyperbinary Expansions and Efficient Algorithms for Stern’s Diatomic Sequence

  • 期刊论文

  • 发表日期：

    2026年7月28日

查看全文
  • Alessandro De Paris

摘要

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 \(m=n\) 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.