The observability of the Fibonacci and the Lucas cubes

  • Authors:
  • Ernesto Dedó;Damiano Torri;Norma Zagaglia Salvi

  • Affiliations:
  • Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

The Fibonacci cube Γn is the graph whose vertices are binary strings of length n without two consecutive 1's and two vertices are adjacent when their Hamming distance is exactly 1. If the binary strings do not contain two consecutive 1's nor a 1 in the first and in the last position, we obtain the Lucas cube Ln. We prove that the observability of Γn and Ln is n, where the observability of a graph G is the minimum number of colors to be assigned to the edges of G so that the coloring is proper and the vertices are distinguished by their color sets.