Recursive fault-tolerance of Fibonacci cube in hypercubes

Gregor, Petr

doi:10.1016/j.disc.2004.09.017

Cited by 16 publications

(19 citation statements)

References 14 publications

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“…These graphs later found applications in mathematical chemistry [15,28] and elsewhere. Fibonacci cubes were studied from algorithmic [9,24] as well as from several other points of view, see [11] and references therein. Lucas cubes [18] form a class of graphs closely related to Fibonacci cubes, in a way they can be considered as a symmetrization of Fibonacci cubes.…”

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confidence: 99%

Cube Polynomial of Fibonacci and Lucas Cubes

Klavžar

Mollard

2011

Acta Appl Math

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The cube polynomial of a graph is the counting polynomial for the number of induced k-dimensional hypercubes (k ≥ 0). We determine the cube polynomial of Fibonacci cubes and Lucas cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular they can be expressed with convolved Fibonacci numbers. Zeros of the studied cube polynomials are explicitly determined. Consequently, the coefficients sequences of cube polynomials of Fibonacci and Lucas cubes are unimodal.

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confidence: 99%

Cube Polynomial of Fibonacci and Lucas Cubes

Klavžar

Mollard

2011

Acta Appl Math

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“…It follows that f f is a factor of α t , t = 1, 2, 3. Denote the copy of f f contained in α 1 , α 2 and α 3 with f (2)…”

Section: Claimmentioning

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“…9 (a). We consider the factors f (2 ′ ) , f (1) and f (2) . Their first coordinates are 2r + |f | + 1, 3r + 1 and 2r + 1 (see Fig.…”

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confidence: 99%

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Proofs of two conjectures on generalized Fibonacci cubes

Wei

Zhang

2016

European Journal of Combinatorics

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“…The fault-tolerance of Fibonacci cubes was studied by Hornh, Jiang, and Kao [16] and Caha and Gregor [6]. Gregor [14] proved c 0 (Γ 3 ) = c 0 (Q 2 ). As an application of our results in Section 2 we prove that for…”

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confidence: 99%

Some Turán type results on the hypercube

Offner

2009

Discrete Mathematics

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a b s t r a c tFor graphs H, G a classical problem in extremal graph theory asks what proportion of the edges of H a subgraph may contain without containing a copy of G. We prove some new results in the case where H is a hypercube. We use a supersaturation technique of Erdős and Simonivits to give a characterization of a set of graphs such that asymptotically the answer is the same when G is a member of this set and when G is a hypercube of some fixed dimension. We apply these results to a specific set of subgraphs of the hypercube called Fibonacci cubes. Additionally, we use a coloring argument to prove new asymptotic bounds on this problem for a different set of graphs. Finally we prove a new asymptotic bound for the case where G is the cube of dimension 3.

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Recursive fault-tolerance of Fibonacci cube in hypercubes

Cited by 16 publications

References 14 publications

Cube Polynomial of Fibonacci and Lucas Cubes

Cube Polynomial of Fibonacci and Lucas Cubes

Proofs of two conjectures on generalized Fibonacci cubes

Some Turán type results on the hypercube

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