12 Hits in 10.5 sec

On median nature and enumerative properties of Fibonacci-like cubes

Sandi Klavžar
2005 Discrete Mathematics  
Fibonacci cubes, extended Fibonacci cubes, and Lucas cubes are induced subgraphs of hypercubes defined in terms of Fibonacci strings. It is shown that all these graphs are median.  ...  Several enumeration results on the number of their edges and squares are obtained. Some identities involving Fibonacci and Lucas numbers are also presented.  ...  Enumerative properties In this section we count the number of edges and squares for each of the Fibonacci cubes, Lucas cubes, and extended Fibonacci cubes.  ... 
doi:10.1016/j.disc.2004.02.023 fatcat:plo2gg4cazdlrklpzkrvwrhpwe

Fibonacci (p, r)-cubes which are median graphs

Lifeng Ou, Heping Zhang
2013 Discrete Applied Mathematics  
It is known that the Fibonacci cubes are median graphs [S. Klavžar, On median nature and enumerative properties of Fibonacci-like cubes, Discrete Math. 299 (2005) 145-153 ].  ...  We show that Fibonacci (p, r)-cubes are median graphs if and only if either r ≤ p and r ≤ 2, or p = 1 and r = n.  ...  Acknowledgments The authors are grateful to the referees for their careful reading and many valuable suggestions.  ... 
doi:10.1016/j.dam.2012.09.008 fatcat:szy45l2wezbqpm5ctyu4kg244y

Author index to volume 299

2005 Discrete Mathematics  
., On the chromatic number of Steiner triple systems of , S., On median nature and enumerative properties of Fibonacci-like cubes (1-3) 145-153 Kobayashi, M., G. Nakamura and C.  ...  Morris, On automorphism groups of circulant digraphs of squarefree order (1-3) 79-98 Dobson, E., On groups of odd prime-power degree that contain a , P. and J.  ... 
doi:10.1016/s0012-365x(05)00408-5 fatcat:opa3uuyl7jhbhgyh7f3icvysli


2005 Discrete Mathematics  
Klavzˇar On median nature and enumerative properties of Fibonacci-like cubes 145 M. Kobayashi, G. Nakamura and C. Nara Uniform coverings of 2-paths with 5-paths in the complete graph 154 Y.  ...  Maureso and J.M. Brunat On endo-Cayley digraphs: The hamiltonian property 194 D.W. Morris, J. Morris and D.P.  ... 
doi:10.1016/s0012-365x(05)00407-3 fatcat:rxvtxpybhzgy3krwwreznodnvy

Cube Polynomial of Fibonacci and Lucas Cubes

Sandi Klavžar, Michel Mollard
2011 Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications  
We determine the cube polynomial of Fibonacci cubes and Lucas cubes, as well as the generating functions for the sequences of these cubes.  ...  Zeros of the studied cube polynomials are explicitly determined. Consequently, the coefficients sequences of cube polynomials of Fibonacci and Lucas cubes are unimodal.  ...  Another motivation for us were several studied of enumerative properties of Fibonacci and Lucas cubes [13, 18, 19] .  ... 
doi:10.1007/s10440-011-9652-4 fatcat:2c4kow6xkjg7zmt3ekvhaojrqq

On the Fibonacci (p,r)-cubes [article]

Jianxin Wei, Yujun Yang, Guangfu Wang
2020 arXiv   pre-print
Then some topological properties of IΓ_n^(p,r) and OΓ_n^(p,r) are studied, including the recursive structure of them, the cubes OΓ_n^(p,r) which are partial cubes and median graphs, some distance invariants  ...  of IΓ_n^(p,r) and OΓ_n^(p,r), and the maximum and minimum degree of these two types of cubes.  ...  Some structural and enumerative properties of the Fibonacci cubes were given in [13] . Fibonacci cubes have already found some applications in chemical graph theory.  ... 
arXiv:1910.05675v2 fatcat:gf4ohe63orc3jmc2frbul2loa4

Fibonacci-like cubes as Z-transformation graphs

Heping Zhang, Lifeng Ou, Haiyuan Yao
2009 Discrete Mathematics  
The Fibonacci cube Γ n is a subgraph of n-dimensional hypercube induced by the vertices without two consecutive ones.  ...  two vertices and joining one to 1010 . . . 10 and the other to 0101 . . . 01.  ...  In network design, the Fibonacci cube is used to emulate hypercube algorithms efficiently. Structural and enumerative properties of the Fibonacci cubes were given in [12] .  ... 
doi:10.1016/j.disc.2008.01.053 fatcat:l7a5vqatmvbd7dnkyo2lulqvkq

Master index to volumes 291-300

2005 Discrete Mathematics  
(2005) 75-90 Kitaev, S., Partially ordered generalized patterns 298 (2005) 212-229 Klavzˇar, S., On median nature and enumerative properties of Fibonacci-like cubes 299 (2005) 145-153 Klavzˇar, S., see  ...  Pe´an, Distributivity properties on P ! ð!  ... 
doi:10.1016/s0012-365x(05)00445-0 fatcat:b5va3kwxz5fufkugwpvscg7oea

The mysterious story of square ice, piles of cubes, and bijections

Ilse Fischer, Matjaž Konvalinka
2020 Proceedings of the National Academy of Sciences of the United States of America  
two-dimensional ice) and their relations to certain classes of plane partitions.  ...  In this paper we tell the story of how the bijections were found.  ...  We are also grateful to the referees for reading the manuscript so carefully and for a number of suggested improvements.  ... 
doi:10.1073/pnas.2005525117 pmid:32879007 fatcat:htmzmvq6pjehngnnbg3sioxw4m

Specification Of Hpc Hardware And Program Components To Enable Further Optimized Mappings

Carlchristian Helmut Johannes Eckert, Wolfgang E Nagel, Jerónimo Castrillón
2016 Zenodo  
Load balancing is one of the key problems in distributed computing.  ...  All data structures are based on widely used libraries and can be interfaced with third-party tools.  ...  Due to the tree-like nature of the consists-of graph, this can reduce the necessary properties to roughly (log p).  ... 
doi:10.5281/zenodo.163329 fatcat:mkb4ewc4nvdfrcclwlqzrbg7ry

Subject Index Volumes 1–200

2001 Discrete Mathematics  
Erdös and Sós, 4925 Erdös and Szekeres, 4879 Erdös et al., 5529, 5888 Erdös Rubin Taylor, 3815 Erdös Sós Turán, 506 Everett, 2901 Faigle and Sands, 2122 Faudree et al., 4399 Faudree Gould Jacobson  ...  Slater, 5299 Hertz and de Werra, 3748 Hibi, 4839 Hoàng, 3748, 4811 Holton, 1660 Holyer and Cockayne, 1118 Howorka, 2636  ...  , see also enumeration aspect, 3112 enumerative combinatorics, 1999, 4027 of Young tableaux, 4702 enumerative formula, 914 invariant, 4839 problem, 2469, 5575, 5618 property, 5097 result, 4623  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Dagstuhl Reports, Volume 8, Issue 11, November 2018, Complete Issue [article]

On behalf of all participants, we would also like to thank Dagstuhl for the high quality facilities provided, for excellent rooms for work and socializing, for the tasty meals, and of course also for the  ...  The organizers of the seminar would also like to thank Ray Siemens and Dan Edelstein for their contributions to the initial Dagstuhl proposal.  ...  The following questions may be of interest. Find enumerative information on the sequences a n and b n , like a closed form or asymptotic behavior.  ... 
doi:10.4230/dagrep.8.11 fatcat:26dpkqaulza4pjp6jqo2u6qqf4