Minimal chordal sense of direction and circulant graphs
Discrete Mathematics
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.cs/0503009,
title = {Minimal chordal sense of direction and circulant graphs},
author = {R. S. C. Leao and V. C. Barbosa},
journal= {arXiv preprint arXiv:cs/0503009},
year = {2007}
}