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Structure of Fibonacci cubes: a survey

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Abstract

The Fibonacci cube Γ n is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1s. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results. Their median nature that leads to a fast recognition algorithm is discussed. The Fibonacci dimension of a graph, studies of graph invariants on Fibonacci cubes, and related classes of graphs are also presented. Along the way some new short proofs are given.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Sandi Klavžar

  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Sandi Klavžar

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  1. Sandi Klavžar
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Correspondence to Sandi Klavžar.

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Klavžar, S. Structure of Fibonacci cubes: a survey. J Comb Optim 25, 505–522 (2013). https://doi.org/10.1007/s10878-011-9433-z

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