Abstract of Paper

Regularity of Congruential Graphs
by Tanguy Urvoy


The aim of this article is to make a link between the congruential systems
investigated by Conway and the infinite graphs theory.  We compare the
graphs of congruential systems with a well known family of infinite graphs:
the regular graphs of finite degree considered by Muller and Shupp, and by
Courcelle. We first consider congruential systems as word rewriting systems
to extract some subfamilies of congruential systems, the
$q$-$p$-congruential systems, representing the regular graphs of finite
degree. We then prove the non-regularity of the Collatz's graph.