Title: Computable Isomorphisms for Certain Classes of Infinite Graphs,
Abstract: We investigate (2,1):1 structures, which consist of a countable set $A$
together with a function $f: A \to A$ such that for every element $x$ in $A$,
$f$ maps either exactly one element or exactly two elements of $A$ to $x$.
These structures extend the notions of injection structures, 2:1 structures,
and (2,0):1 structures studied by Cenzer, Harizanov, and Remmel, all of which
can be thought of as infinite directed graphs. We look at various
computability-theoretic properties of (2,1):1 structures, most notably that of
computable categoricity. We say that a structure $\mathcal{A}$ is computably
categorical if there exists a computable isomorphism between any two computable
copies of $\mathcal{A}$. We give a sufficient condition under which a (2,1):1
structure is computably categorical, and present some examples of (2,1):1
structures with different computability-theoretic properties.