The shortest path problem in the Knödel graph
The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance b...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Grigoryan, Hayk [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Schlagwörter: |
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| Umfang: |
8 |
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| Übergeordnetes Werk: |
Enthalten in: Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst - 2012transfer abstract, JDA, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:31 ; year:2015 ; pages:40-47 ; extent:8 |
| Links: |
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| DOI / URN: |
10.1016/j.jda.2014.11.008 |
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ELV039682641 |
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| 520 | |a The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. | ||
| 520 | |a The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. | ||
| 650 | 7 | |a Shortest path problem |2 Elsevier | |
| 650 | 7 | |a Diameter of the Knödel graph |2 Elsevier | |
| 650 | 7 | |a Knödel graph |2 Elsevier | |
| 700 | 1 | |a Harutyunyan, Hovhannes A. |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |t Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst |d 2012transfer abstract |d JDA |g Amsterdam [u.a.] |w (DE-627)ELV026326809 |
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10.1016/j.jda.2014.11.008 doi GBVA2015007000009.pica (DE-627)ELV039682641 (ELSEVIER)S1570-8667(14)00093-8 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 540 VZ 610 VZ 44.90 bkl Grigoryan, Hayk verfasserin aut The shortest path problem in the Knödel graph 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. Shortest path problem Elsevier Diameter of the Knödel graph Elsevier Knödel graph Elsevier Harutyunyan, Hovhannes A. oth Enthalten in Elsevier Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst 2012transfer abstract JDA Amsterdam [u.a.] (DE-627)ELV026326809 volume:31 year:2015 pages:40-47 extent:8 https://doi.org/10.1016/j.jda.2014.11.008 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_72 GBV_ILN_613 44.90 Neurologie VZ AR 31 2015 40-47 8 045F 510 |
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10.1016/j.jda.2014.11.008 doi GBVA2015007000009.pica (DE-627)ELV039682641 (ELSEVIER)S1570-8667(14)00093-8 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 540 VZ 610 VZ 44.90 bkl Grigoryan, Hayk verfasserin aut The shortest path problem in the Knödel graph 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. Shortest path problem Elsevier Diameter of the Knödel graph Elsevier Knödel graph Elsevier Harutyunyan, Hovhannes A. oth Enthalten in Elsevier Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst 2012transfer abstract JDA Amsterdam [u.a.] (DE-627)ELV026326809 volume:31 year:2015 pages:40-47 extent:8 https://doi.org/10.1016/j.jda.2014.11.008 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_72 GBV_ILN_613 44.90 Neurologie VZ AR 31 2015 40-47 8 045F 510 |
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10.1016/j.jda.2014.11.008 doi GBVA2015007000009.pica (DE-627)ELV039682641 (ELSEVIER)S1570-8667(14)00093-8 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 540 VZ 610 VZ 44.90 bkl Grigoryan, Hayk verfasserin aut The shortest path problem in the Knödel graph 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. Shortest path problem Elsevier Diameter of the Knödel graph Elsevier Knödel graph Elsevier Harutyunyan, Hovhannes A. oth Enthalten in Elsevier Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst 2012transfer abstract JDA Amsterdam [u.a.] (DE-627)ELV026326809 volume:31 year:2015 pages:40-47 extent:8 https://doi.org/10.1016/j.jda.2014.11.008 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_72 GBV_ILN_613 44.90 Neurologie VZ AR 31 2015 40-47 8 045F 510 |
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10.1016/j.jda.2014.11.008 doi GBVA2015007000009.pica (DE-627)ELV039682641 (ELSEVIER)S1570-8667(14)00093-8 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 540 VZ 610 VZ 44.90 bkl Grigoryan, Hayk verfasserin aut The shortest path problem in the Knödel graph 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. Shortest path problem Elsevier Diameter of the Knödel graph Elsevier Knödel graph Elsevier Harutyunyan, Hovhannes A. oth Enthalten in Elsevier Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst 2012transfer abstract JDA Amsterdam [u.a.] (DE-627)ELV026326809 volume:31 year:2015 pages:40-47 extent:8 https://doi.org/10.1016/j.jda.2014.11.008 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_72 GBV_ILN_613 44.90 Neurologie VZ AR 31 2015 40-47 8 045F 510 |
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10.1016/j.jda.2014.11.008 doi GBVA2015007000009.pica (DE-627)ELV039682641 (ELSEVIER)S1570-8667(14)00093-8 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 540 VZ 610 VZ 44.90 bkl Grigoryan, Hayk verfasserin aut The shortest path problem in the Knödel graph 2015transfer abstract 8 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. Shortest path problem Elsevier Diameter of the Knödel graph Elsevier Knödel graph Elsevier Harutyunyan, Hovhannes A. oth Enthalten in Elsevier Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst 2012transfer abstract JDA Amsterdam [u.a.] (DE-627)ELV026326809 volume:31 year:2015 pages:40-47 extent:8 https://doi.org/10.1016/j.jda.2014.11.008 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_72 GBV_ILN_613 44.90 Neurologie VZ AR 31 2015 40-47 8 045F 510 |
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Enthalten in Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst Amsterdam [u.a.] volume:31 year:2015 pages:40-47 extent:8 |
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Enthalten in Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst Amsterdam [u.a.] volume:31 year:2015 pages:40-47 extent:8 |
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Improvement the promotional efficiency of Ru by controlling the position and distribution of RuO2 precursors on CoRu/SiO2 catalyst |
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The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. |
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The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. |
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The Knödel graph W Δ , n is a graph of even order n and degree Δ where 2 ≤ Δ ≤ ⌊ log 2 n ⌋ . Most properties of the Knödel graph are known only for W Δ , 2 Δ and W Δ − 1 , 2 Δ − 2 . In this paper we study the shortest path problem in W Δ , n for all Δ and n. We give a tight bound on the distance between any two vertices in W Δ , n . We show that for almost all Δ, the presented bound differs from actual distance by at most 2. The proofs are constructive and allow us to present an O ( log n ) time algorithm to construct a short path between any pair of vertices in W Δ , n . The diameter of W Δ , n is known only for n = 2 Δ . Using our results on the shortest path problem, we present tight upper and lower bounds on the diameter of the Knödel graph for all Δ and n. |
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