The generalized Fibonacci cube $Q_h(f)$ is the graph obtained from the $h$-cube $Q_h$ by removing all vertices that contain a given binary string $f$ as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube $Q_h(111)$ is the set of all binary strings $b_1b_2 \ldots b_h$ containing no three consecutive 1's. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time.

Source : oai:HAL:hal-01364442v1

Volume: Vol. 17 no. 3

Section: Graph Theory

Published on: September 3, 2016

Submitted on: January 12, 2015

Keywords: generalized Fibonacci cube,3rd order generalized Fibonacci cube,characterization,recognition algorithm,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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