The structures of bad words
The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest in...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wei, Jianxin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017transfer abstract |
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| Umfang: |
11 |
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| Übergeordnetes Werk: |
Enthalten in: Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells - Wang, Qiang ELSEVIER, 2015transfer abstract, London |
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| Übergeordnetes Werk: |
volume:59 ; year:2017 ; pages:204-214 ; extent:11 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.ejc.2016.05.003 |
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| 520 | |a The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . | ||
| 520 | |a The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . | ||
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10.1016/j.ejc.2016.05.003 doi GBVA2017007000029.pica (DE-627)ELV035799137 (ELSEVIER)S0195-6698(16)30022-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 620 VZ 610 VZ 44.94 bkl Wei, Jianxin verfasserin aut The structures of bad words 2017transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . Enthalten in Academic Press Wang, Qiang ELSEVIER Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells 2015transfer abstract London (DE-627)ELV013014358 volume:59 year:2017 pages:204-214 extent:11 https://doi.org/10.1016/j.ejc.2016.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_40 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 59 2017 204-214 11 045F 510 |
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10.1016/j.ejc.2016.05.003 doi GBVA2017007000029.pica (DE-627)ELV035799137 (ELSEVIER)S0195-6698(16)30022-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 620 VZ 610 VZ 44.94 bkl Wei, Jianxin verfasserin aut The structures of bad words 2017transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . Enthalten in Academic Press Wang, Qiang ELSEVIER Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells 2015transfer abstract London (DE-627)ELV013014358 volume:59 year:2017 pages:204-214 extent:11 https://doi.org/10.1016/j.ejc.2016.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_40 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 59 2017 204-214 11 045F 510 |
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10.1016/j.ejc.2016.05.003 doi GBVA2017007000029.pica (DE-627)ELV035799137 (ELSEVIER)S0195-6698(16)30022-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 620 VZ 610 VZ 44.94 bkl Wei, Jianxin verfasserin aut The structures of bad words 2017transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . Enthalten in Academic Press Wang, Qiang ELSEVIER Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells 2015transfer abstract London (DE-627)ELV013014358 volume:59 year:2017 pages:204-214 extent:11 https://doi.org/10.1016/j.ejc.2016.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_40 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 59 2017 204-214 11 045F 510 |
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10.1016/j.ejc.2016.05.003 doi GBVA2017007000029.pica (DE-627)ELV035799137 (ELSEVIER)S0195-6698(16)30022-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 620 VZ 610 VZ 44.94 bkl Wei, Jianxin verfasserin aut The structures of bad words 2017transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . Enthalten in Academic Press Wang, Qiang ELSEVIER Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells 2015transfer abstract London (DE-627)ELV013014358 volume:59 year:2017 pages:204-214 extent:11 https://doi.org/10.1016/j.ejc.2016.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_40 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 59 2017 204-214 11 045F 510 |
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10.1016/j.ejc.2016.05.003 doi GBVA2017007000029.pica (DE-627)ELV035799137 (ELSEVIER)S0195-6698(16)30022-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 620 VZ 610 VZ 44.94 bkl Wei, Jianxin verfasserin aut The structures of bad words 2017transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . Enthalten in Academic Press Wang, Qiang ELSEVIER Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells 2015transfer abstract London (DE-627)ELV013014358 volume:59 year:2017 pages:204-214 extent:11 https://doi.org/10.1016/j.ejc.2016.05.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_40 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 59 2017 204-214 11 045F 510 |
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Assessment of five different cathode materials for Co(II) reduction with simultaneous hydrogen evolution in microbial electrolysis cells |
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The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . |
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The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . |
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The generalized Fibonacci cube Q d ( f ) is the graph obtained from the hypercube Q d by removing all vertices that contain a given binary word f . A word f is called good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1 , and bad otherwise. The index B ( f ) of a word f is the smallest integer d such that Q d ( f ) is not an isometric subgraph of Q d . Klavžar and Shpectorov showed that a bad word has a 2-error overlap. In this paper, we show that if a word has a 2-error overlap then it is bad, and we characterize the structures of all bad words. Ilić, Klavžar and Rho showed that a word f is bad if there exist p -critical words for Q d ( f ) for some d . We find that a word is bad if and only if there exists only a pair of 2-critical words, or only a pair of 3-critical words, or both only a pair of 2-critical words and only a pair of 3-critical words for Q B ( f ) ( f ) . We also design an O ( | f | 3 ) algorithm which can output the index B ( f ) of f , and give all pairs of p -critical words for Q B ( f ) ( f ) . |
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