485 research outputs found
Minimal chordal sense of direction and circulant graphs
A sense of direction is an edge labeling on graphs that follows a globally
consistent scheme and is known to considerably reduce the complexity of several
distributed problems. In this paper, we study a particular instance of sense of
direction, called a chordal sense of direction (CSD). In special, we identify
the class of k-regular graphs that admit a CSD with exactly k labels (a minimal
CSD). We prove that connected graphs in this class are Hamiltonian and that the
class is equivalent to that of circulant graphs, presenting an efficient
(polynomial-time) way of recognizing it when the graphs' degree k is fixed
Shared Rough and Quasi-Isometries of Groups
We present a variation of quasi-isometry to approach the problem of defining
a geometric notion equivalent to commensurability. In short, this variation can
be summarized as "quasi-isometry with uniform parameters for a large enough
family of generating systems". Two similar notions (using isometries and rough
isometries instead, respectively) are presented alongside.
This article is based mainly on a chapter of the author's doctoral thesis
(\cite{Lochmann_dissertation}).Comment: 16 page
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