超二进制展开图的同构性与Stern二原子序列的高效算法
Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence
AI总结：
该研究针对非负整数的超二进制展开对应的边标记有向图$A(n)$，分析其圈秩与结构，证明偶数阶图的同构唯一性，推导Stern二原子序列相关公式并讨论相关算法。
摘要：
为研究非负整数$n$的超二进制展开，近期学界引入了一种边标记有向图$A(n)$。我们先指出关于其圈秩的若干新的简单结论，随后给出该图结构的相对简洁描述，并证明：若$m$、$n$均为偶数，且$A(n)$与$A(m)$作为边标记图同构，则$m=n$。我们还从$A(n)$的结构推导出一个与Stern二原子序列相关的公式，并以同样的思路讨论了近期文献中出现的一些算法。
英文摘要：
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 $m=n$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
