Minimal chordal sense of direction and circulant graphs

Authors:
Rodrigo S. C. Leão;Valmir C. Barbosa
Affiliations:
Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil;Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
Venue:
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Year:
2006

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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 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.