Results 41 to 50 of about 173 (142)
On isomorphism classes of generalized Fibonacci cubes
European Journal of Combinatorics, 2016 The generalized Fibonacci cube $Q_d(f)$ is the subgraph of the $d$-cube $Q_d$ induced on the set of all strings of length $d$ that do not contain $f$ as a substring. It is proved that if $Q_d(f) \cong Q_d(f')$ then $|f|=|f'|$. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrelation polynomial associated to a binary
Azarija, Jernej +4 more
openaire +3 more sources
Computing Some Topological Indices of Two Kinds of Dendrimer Graphs G[n] and H[n]
Journal of Mathematics, Volume 2024, Issue 1, 2024.Dendrimer molecules are macromolecules which have many applications in nanosciences, drug delivery, biology, and different areas of sciences. Topological indices of chemical graph theory are numerical descriptor of a molecular structure. The dendrimer graph G[n] is obtained by attaching the new paths P9, joined each pendant vertex of G[n − 1] to ...
Hojat Kaviani +2 more
wiley +1 more source
The parameters of Fibonacci and Lucas cubes
Ars Mathematica Contemporanea, 2016 Motivated by the conjectures from Castro, et al. in 2011, in this paper we use integer programming formulations for computing the domination number, the 2-packing number and the independent domination number of Fibonacci cubes and Lucas cubes for n ≤ 13 .
Ilić, Aleksandar, Milošević, Marko
openaire +3 more sources
FIBONACCI NUMBERS MODULO CUBES OF PRIMES
Taiwanese Journal of Mathematics, 2013 Let $p$ be an odd prime. It is well known that $F_{p-(\frac p5)}\equiv 0\pmod{p}$, where $\{F_n\}_{n\ge0}$ is the Fibonacci sequence and $(-)$ is the Jacobi symbol. In this paper we show that if $p\not=5$ then we may determine $F_{p-(\frac p5)}$ mod $p^3$ in the following way: $$\sum_{k=0}^{(p-1)/2}\frac{\binom{2k}k}{(-16)^k}\equiv\left(\frac{p}5\right)
openaire +3 more sources
Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map. [PDF]
Entropy (Basel), 2023 Wang L, Ran Q, Ding J.
europepmc +1 more source
Observability of the extended Fibonacci cubes
Discrete Mathematics, 2003 The Fibonacci cube \(\Gamma_n\) is the subgraph of the hypercube \(Q_n\) induced by the set of Fibonacci strings of order \(n\). By \(\text{obs}(G)\) we mean the minimum number of colours required for a strong edge colouring of \(G\). Let \(i\), \(n\) be positive integers with \(n\geq i+2\). The authors show that \(\text{obs}(\Gamma^i_n)= n+1\) for \(i=
C. Whitehead, ZAGAGLIA, NORMA
openaire +2 more sources
Optimal cube factors of Fibonacci and matchable Lucas cubes
, 2018 The optimal cube factor of a graph, a special kind of component factor, is first introduced. Furthermore, the optimal cube factors of Fibonacci and matchable Lucas cubes are studied; and some results on the Padovan sequence and binomial coefficients are obtained.
Wang, Xu, Zhao, Xuxu, Yao, Haiyuan
openaire +2 more sources
$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes
The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive 1s. We study a one parameter generalization, p-th order Fibonacci cubes $Γ^{(p)}_n$, which are subgraphs of $Q_n$ induced by strings without p consecutive 1s. We show the link between vertices of $Γ^{(p)}_n$ and compositions of integers with parts in
openaire +2 more sources
Magnetic dynamics of hedgehog in icosahedral quasicrystal. [PDF]
Sci Rep, 2022 Watanabe S.
europepmc +1 more source
On the Fibonacci $(p,r)$-cubes
, 2019 In this paper, first it is shown that the "FSibonacci $(p,r)$-cube"(denoted as $I _{n}^{(p,r)}$) studied in many papers, such as \cite{OZY}, \cite{K1}, \cite{OZ}, \cite{KR} and \cite{JZ}, is a new topological structure different from the original one (denoted as $O _{n}^{(p,r)}$) presented by Egiazarian and Astola $\cite{EA}$.
Wei, Jianxin, Yang, Yujun, Wang, Guangfu
openaire +2 more sources