| Title: | Connectivity of Fibonacci cubes, Lucas cubes, and generalized cubes |
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| Authors: | ID Azarija, Jernej (Author)
ID Klavžar, Sandi (Author)
ID Lee, Jaehun (Author)
ID Rho, Yoomi (Author) |
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| Files: |  Discrete_Mathematics_&_Theoretical_Computer_Science_2015_Azarija_et_al._Connectivity_of_Fibonacci_cubes,_Lucas_cubes,_and_generalized_cu.pdf (740,04 KB)
MD5: 05275ACF191765822279C45779297063
PID: 20.500.12556/dkum/a74b33cb-763b-4c5f-97e8-596f10d3a5dc
 http://dmtcs.episciences.org/2115
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | If ▫$f$▫ is a binary word and ▫$d$▫ a positive integer, then the generalized Fibonacci cube ▫$Q_d(f)$▫ is the graph obtained from the ▫$d$▫-cube ▫$Q_d$▫ by removing all the vertices that contain ▫$f$▫ as a factor, while the generalized Lucas cube ▫$Q_d(\stackrel{\leftharpoondown}{f})$▫ is the graph obtained from ▫$Q_d$▫ by removing all the vertices that have a circulation containing ▫$f$▫ as a factor. The Fibonacci cube ▫$\Gamma_d$▫ and the Lucas cube ▫$\Lambda_d$▫ are the graphs ▫$Q_d({11})$▫ and ▫$Q_d(\stackrel{\leftharpoondown}{11})$▫, respectively. It is proved that the connectivity and the edge-connectivity of ▫$\Gamma_d$▫ as well as of ▫$\Lambda_d$▫ are equal to ▫$\left\lfloor \frac{d+2}{3}\right\rfloor$▫. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all ▫$f$▫ and all ▫$d \le9$▫. |
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| Keywords: | Fibonacci cube, Lucas cube, generalized Fibonacci cube, generalized Lucas cube, connectivity, combinatorics on words |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 01.10.2014 |
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| Article acceptance date: | 28.01.2015 |
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| Publication date: | 04.02.2015 |
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| Publisher: | Discrete Mathematics & Theoretical Computer Science |
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| Year of publishing: | 2015 |
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| Number of pages: | Str. 79-88 |
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| Numbering: | Letn. 17, št. 1 |
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| PID: | 20.500.12556/DKUM-66780  |
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| ISSN: | 1365-8050 |
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| UDC: | 519.17:004 |
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| ISSN on article: | 1365-8050 |
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| COBISS.SI-ID: | 17220697 |
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| NUK URN: | URN:SI:UM:DK:0XCNAHN9 |
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| Publication date in DKUM: | 10.07.2017 |
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| Views: | 1522 |
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| Downloads: | 220 |
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| Metadata: |    |
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| Categories: | Misc.
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