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 analyze 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Leão, R. S. C., & Barbosa, V. C. (2006). Minimal chordal sense of direction and circulant graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4162 LNCS, pp. 670–680). Springer Verlag. https://doi.org/10.1007/11821069_58
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