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Observability of the extended Fibonacci cubes

2003
*
Discrete Mathematics
*

A

doi:10.1016/s0012-365x(02)00824-5
fatcat:2nwe4ryoonfuxip2hxrkcfz6da
*Fibonacci*string*of*order n is a binary string*of*length n with no two consecutive ones.*The**Fibonacci**cube*n is*the*subgraph*of**the*hypercube Qn induced by*the*set*of**Fibonacci*strings*of*order n. ... For positive integers i; n, with n ¿ i,*the*ith*extended**Fibonacci**cube*is*the*vertex induced subgraph*of*Qn for which V ( i n ) = V i n is deÿned recursively by with initial conditions V i i = Bi, V i ...*The**extended**Fibonacci**cubes*, introduced by Wu [13] , are constructed by*the*same recursive relation as*the**Fibonacci**cube*, but with di erent initial conditions. ...##
###
On median nature and enumerative properties of Fibonacci-like cubes

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. ...

*Observe*also that 0 n = n .

*The*

*Fibonacci*

*cubes*4 and 5 ,

*the*Lucas

*cube*5 , and

*the*

*extended*

*Fibonacci*

*cube*1 4 , are, together with

*the*corresponding vertex labels, shown in Fig. 1 . ...

##
###
Structure of Fibonacci cubes: a survey

2011
*
Journal of combinatorial optimization
*

*The*

*Fibonacci*

*cube*Γ n is

*the*subgraph

*of*

*the*n-

*cube*induced by

*the*binary strings that contain no two consecutive 1s. ...

*The*

*Fibonacci*dimension

*of*a graph, studies

*of*graph invariants on

*Fibonacci*

*cubes*, and related classes

*of*graphs are also presented. Along

*the*way some new short proofs are given. ... This work was supported in part by

*the*Ministry

*of*Science

*of*Slovenia under

*the*grant P1-0297. ...

##
###
A Fault-Tolerant Routing Strategy for Fibonacci-Class Cubes
[chapter]

2005
*
Lecture Notes in Computer Science
*

*Fibonacci*

*Cubes*(FCs), together with

*the*enhanced and

*extended*forms, are a family

*of*interconnection topologies formed by diluting links from binary hypercube. ... Finally,

*the*performance

*of*

*the*algorithm is presented and analyzed through software simulation, showing its feasibility. ... In Figure 4 , it can be

*observed*that

*the*average latency

*of*regular/Enhanced/

*Extended*

*Fibonacci*

*Cubes*increases when

*the*networks dimension n is below 19. ...

##
###
On domination-type invariants of Fibonacci cubes and hypercubes

2017
*
Ars Mathematica Contemporanea
*

*The*

*Fibonacci*

*cube*Γ n is

*the*subgraph

*of*

*the*n-dimensional

*cube*Q n induced by

*the*vertices that contain no two consecutive 1s. ... Using integer linear programming exact values for

*the*2packing number, connected domination number, paired domination number, and signed domination number

*of*small

*Fibonacci*

*cubes*and hypercubes are obtained ... Acknowledgment

*The*authors acknowledge

*the*financial support from

*the*Slovenian Research Agency (research code funding No. P1-0297) and from

*the*Basic Science Research Program through ...

##
###
Generalized Fibonacci and Lucas cubes arising from powers of paths and cycles

2016
*
Discrete Mathematics
*

For h=1 such a diagram is called a

doi:10.1016/j.disc.2015.08.012
fatcat:lhj2hfcvcfblfpadgsqgrtqeau
*Fibonacci**cube*, and for h>1 we obtain a generalization*of**the**Fibonacci**cube*. ... Then, we show that*the*number*of*edges*of*a generalized*Fibonacci**cube*is obtained by convolution*of*an h-*Fibonacci*sequence with itself. In*the*second part we consider*the*case*of*cycles. ... Acknowledgment We are grateful to*the*editor for is precious work, and to*the*anonymous referee for a careful reading*of*our paper, and for his/her helpful suggestions which allowed us to improve*the*presentation ...##
###
Fibonacci-run graphs I: basic properties
[article]

2021
*
arXiv
*
pre-print

They have

arXiv:2010.05518v3
fatcat:sttqzwxoz5c2xcptxmki6rjl4a
*the*same number*of*vertices as*Fibonacci**cubes*, but fewer edges and different connectivity properties. ... Among*the*classical models for interconnection networks are hypercubes and*Fibonacci**cubes*. ... Sandi Klavžar for enabling*the*cooperation*of**the*authors*of*this article, and his early interest in*the*topic.*The*first author would like ...##
###
Θ-graceful labelings of partial cubes

2006
*
Discrete Mathematics
*

*The*Cartesian product

*of*-graceful partial

*cubes*is again such and we wonder whether in fact any partial

*cube*is -graceful. ... It is shown that several classes

*of*partial

*cubes*are -graceful, for instance even cycles,

*Fibonacci*

*cubes*, and (newly introduced) lexicographic subcubes. ... For every n i 0,

*the*

*extended*

*Fibonacci*

*cube*i n is a -graceful partial

*cube*. ...

##
###
Cube Polynomial of Fibonacci and Lucas Cubes

2011
*
Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications
*

We determine

doi:10.1007/s10440-011-9652-4
fatcat:2c4kow6xkjg7zmt3ekvhaojrqq
*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. ... Hence understanding*the**cube*polynomial*of**Fibonacci**cubes*and how it behaves under*the*Cartesian multiplication, one can obtain all*the*corresponding results for*the**extended**Fibonacci**cubes*as well. ...##
###
On the Wiener index of generalized Fibonacci cubes and Lucas cubes

2015
*
Discrete Applied Mathematics
*

In this paper

doi:10.1016/j.dam.2015.02.002
fatcat:263xpci5hvhupc7zj3hzq7go7i
*the*Wiener index*of*Q d (1 s ) and*the*Wiener index*of*Q d ( ↽ 1 s ) are expressed as functions*of**the*order*of**the*generalized*Fibonacci**cubes*. ...*The*generalized*Fibonacci**cube*Q d (f ) is*the*graph obtained from*the*d-*cube*Q d by removing all vertices that contain a given binary word f as a factor;*the*generalized Lucas*cube*Q d ( ↽ f ) is obtained ...*the*National Research Foundation*of*Korea funded by*the*Ministry*of*Education, Science and Technology grant 2011-00253195. ...##
###
Exploration of Fibonacci Function

2012
*
Bulletin of Mathematical Sciences and Applications
*

Also, I defined

doi:10.18052/www.scipress.com/bmsa.1.57
fatcat:7rphko7ctvbllejbc6mkndjdoa
*the*limit value*of**Fibonacci*function, which is closed to 1.618... where x tends to infinity. Including,*Fibonacci*sum as well. ... In this paper, I define*Fibonacci*function (probably unknown) on Real number field, for all x∈R, F:R → R,э F (x+n) = ∫nF(x+1)+∫n-1F(x). ... Nicolas, whose encouragement, guidance and support from*the*initial to*the*final level enabled me to develop an understanding*of**the*subject. ...##
###
Recursive fault-tolerance of Fibonacci cube in hypercubes

2006
*
Discrete Mathematics
*

If we remove from

doi:10.1016/j.disc.2004.09.017
fatcat:jauwe5zphbeoxpjav5rcgf46sq
*Fibonacci**cube**the*vertices with 1 both in*the*first and*the*last position, we obtain Lucas*cube*. ... We consider*the*problem*of*determining*the*minimum number*of*vertices in n-dimensional hypercube whose removal leaves no subgraph isomorphic to m-dimensional*Fibonacci**cube*. ... Acknowledgment*The*author wishes to thank V. Koubek for his encouragement and helpful discussions and P. Kolman and anonymous referee for their comments. ...##
###
Daisy cubes and distance cube polynomial

2018
*
European journal of combinatorics (Print)
*

Daisy

doi:10.1016/j.ejc.2018.02.019
fatcat:gayjzhdgiff3dp6yyykv5eajom
*cubes*are partial*cubes*that include*Fibonacci**cubes*, Lucas*cubes*, and bipartite wheels. ... Then*the*daisy*cube*Q n (X) is introduced as*the*subgraph*of*Q n induced by*the*intersection*of**the*intervals I(x, 0 n ) over all x ∈ X. ...*The**Fibonacci**cube*Γ n , n ≥ 1, is*the*subgraph*of*Q n induced by*the**Fibonacci*words*of*length n. A*Fibonacci*word u 1 . . . u n is a Lucas word if in addition u 1 · u n = 0 holds. ...##
###
Daisy cubes and distance cube polynomial
[article]

2017
*
arXiv
*
pre-print

Daisy

arXiv:1705.08674v1
fatcat:yddy62q7zbcfhptqqqtabpgpky
*cubes*are partial*cubes*that include*Fibonacci**cubes*, Lucas*cubes*, and bipartite wheels. ... Then*the*daisy*cube*Q n (X) is introduced as*the*sub-graph*of*Q n induced by*the*intersection*of**the*intervals I(x, 0 n) over all x ∈ X. ...*The**Fibonacci**cube*Γ n , n ≥ 1, is*the*subgraph*of*Q n induced by*the**Fibonacci*words*of*length n. A*Fibonacci*word u 1 . . . u n is a Lucas word if in addition u 1 · u n = 0 holds. ...##
###
$q$-counting hypercubes in Lucas cubes

2018
*
Turkish Journal of Mathematics
*

Acknowledgment This work was done while

doi:10.3906/mat-1605-2
fatcat:a5sgbbln4rfb7odvdetbsrzpbi
*the*first author was visiting Koç Lab at*the*Department*of*Computer Science, University*of*California Santa Barbara. ...*The*authors would like to thank*the*anonymous reviewers for their valuable comments. ... We note that many*of**the*results presented here*extend*those*of*Klavžar and Mollard [5] , as C(Λ n , x; q) is a refinement*of**the**cube*polynomial C(Λ n , x) . ...
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