Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence

To investigate hyperbinary expansions of a nonnegative integer n, an edge-labelled 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-labelled graphs, then m=n. From the structure of A(n) we also derive a formula and an efficient algorithm for the Stern's diatomic sequence.