Results 11 to 20 of about 906 (135)
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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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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Vertex and Edge Orbits of Fibonacci and Lucas Cubes [PDF]
Annals of Combinatorics, 2016 The Fibonacci cube $Γ_n$ is obtained from the $n$-cube $Q_n$ by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube $Λ_n$ is obtained. The number of vertex and edge orbits, the sets of the sizes of the orbits, and the number of orbits of each size, are determined
Jernej Azarija +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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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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Generalized Fibonacci and Lucas cubes arising from powers of paths and cycles
Discrete Mathematics, 2016 19 pages.
Pietro Codara
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Distance cube polynomials of Fibonacci and Lucas-run graphs
Discrete Applied MathematicsThe Fibonacci-run graphs $\mathcal{R}_n$ are a family of an induced subgraph of hypercubes introduced by Eğecioğlu and Iršič in 2021. A cyclic version of $\mathcal{R}_n$, the Lucas-run graph $\mathcal{R}_n^l$, was also recently proposed (Jianxin Wei, 2024). We prove that the generating function previously given for the polynomial $D_{\mathcal{R}_n}(x,q)
Michel Mollard
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The Mostar Index of Fibonacci and Lucas Cubes [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 The Mostar index of a graph was defined by Došlić, Martinjak, Škrekovski, Tipurić Spužević and Zubac in the context of the study of the properties of chemical graphs. It measures how far a given graph is from being distance-balanced. In this paper, we determine the Mostar index of two well-known families of graphs: Fibonacci cubes and Lucas cubes.
Ömer Eğecioğlu +2 more
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International Journal of Foundations of Computer Science, 2021 We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes.
Ömer Egecioglu +2 more
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Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and alternate Lucas cubes
Discrete Mathematics, Algorithms and Applications, 2023 The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter is called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices is referred as diametral paths.
Ömer Egecioglu +2 more
openaire +4 more sources