Structure of Fibonacci cubes: a survey

Sandi Klavžar ()
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Sandi Klavžar: University of Ljubljana

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 3, 505-522

Abstract: 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.

Keywords: Fibonacci cube; Fibonacci number; Cartesian product of graphs; Median graph; Degree sequence; Cube polynomial (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-011-9433-z

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