Results 111 to 120 of about 515 (134)
Asymptotic Properties of Fibonacci Cubes and Lucas Cubes [PDF]
Annals of Combinatorics, 2014 It is proved that the asymptotic average eccentricity and the asymptotic average degree of Fibonacci cubes and Lucas cubes are $(5+\sqrt 5)/10$ and $(5-\sqrt 5)/5$, respectively. A new labeling of the leaves of Fibonacci trees is introduced and proved that the eccentricity of a vertex of a given Fibonacci cube is equal to the depth of the associated ...
Sandi Klavžar +2 more
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Maximal hypercubes in Fibonacci and Lucas cubes
Discrete Applied Mathematics, 2012 The Fibonacci cube $Γ_n$ is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $Λ_n$ is obtained from $Γ_n$ by removing vertices that start and end with 1. We characterize maximal induced hypercubes in $Γ_n$ and $Λ_n$ and deduce for any $p\leq n$ the number of maximal $p$-dimensional ...
Michel Mollard
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The eccentricity sequences of Fibonacci and Lucas cubes
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michel Mollard
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On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes
Computers and Mathematics With Applications, 2011 Let $\Gamma_n$ and $\Lambda_n$ be the $n$-dimensional Fibonacci cube and Lucas cube, respectively. The domination number $\gamma$ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that $\gamma(\Lambda_{n})$ is bounded below by $\left\lceil\frac{L_{n}-2n}{n-3}\right\rceil$, where $L_n$ is the $n$-th Lucas number.
Sandi Klavžar +2 more
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On the Wiener index of generalized Fibonacci cubes and Lucas cubes
Discrete Applied Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sandi Klavžar, Yoomi Rho
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The degree sequence of Fibonacci and Lucas cubes
Discrete Mathematics, 2011 The Fibonacci cube $\Gamma_n$ is the subgraph of the $n$-cube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $\Lambda_n$ is obtained from $\Gamma_n$ by removing vertices that start and end with 1. It is proved that the number of vertices of degree $k$ in $\Gamma_n$ and $\Lambda_n$ is $\sum_{i = 0}^k \binom{n-2i}{k-i} \
Sandi Klavžar +2 more
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Edge General Position Sets in Fibonacci and Lucas Cubes
Bulletin of the Malaysian Mathematical Sciences Society, 2023 AbstractA set of edges$$X\subseteq E(G)$$X⊆E(G)of a graphGis an edge general position set if no three edges fromXlie on a common shortest path inG. The cardinality of a largest edge general position set ofGis the edge general position number ofG. In this paper, edge general position sets are investigated in partial cubes.
Sandi Klavžar, Klavžar Sandi
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The Irregularity Polynomials of Fibonacci and Lucas cubes
Bulletin of the Malaysian Mathematical Sciences Society, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elif Saygi, Ömer Eğecioğlu
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$q$-counting hypercubes in Lucas cubes
Turkish Journal of Mathematics, 2018 Summary: Lucas and Fibonacci cubes are special subgraphs of the binary hypercubes that have been proposed as models of interconnection networks. Since these families are closely related to hypercubes, it is natural to consider the nature of the hypercubes they contain.
Ömer Eğecioğlu
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