Pretty good state transfer on Cayley graphs over dihedral groups

The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t )...
Ausführliche Beschreibung

The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that | e v t H ( t ) e u | ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Cao, Xiwang [verfasserIn] Wang, Dandan [verfasserIn] Feng, Keqin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph

Übergeordnetes Werk:	Enthalten in: Discrete mathematics - Amsterdam [u.a.] : Elsevier, 1971, 343
Übergeordnetes Werk:	volume:343

DOI / URN:	10.1016/j.disc.2019.111636

Katalog-ID:	ELV003251683

Internformat


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520			\|a The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST.
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951			\|a AR
952			\|d 343

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matchkey_str	caoxiwangwangdandanfengkeqin:2019----:rtyodtttaseocyegaho
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publishDate	2019
allfields	10.1016/j.disc.2019.111636 doi (DE-627)ELV003251683 (ELSEVIER)S0012-365X(19)30306-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Cao, Xiwang verfasserin aut Pretty good state transfer on Cayley graphs over dihedral groups 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph Wang, Dandan verfasserin aut Feng, Keqin verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
spelling	10.1016/j.disc.2019.111636 doi (DE-627)ELV003251683 (ELSEVIER)S0012-365X(19)30306-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Cao, Xiwang verfasserin aut Pretty good state transfer on Cayley graphs over dihedral groups 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph Wang, Dandan verfasserin aut Feng, Keqin verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfields_unstemmed	10.1016/j.disc.2019.111636 doi (DE-627)ELV003251683 (ELSEVIER)S0012-365X(19)30306-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Cao, Xiwang verfasserin aut Pretty good state transfer on Cayley graphs over dihedral groups 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph Wang, Dandan verfasserin aut Feng, Keqin verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfieldsGer	10.1016/j.disc.2019.111636 doi (DE-627)ELV003251683 (ELSEVIER)S0012-365X(19)30306-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Cao, Xiwang verfasserin aut Pretty good state transfer on Cayley graphs over dihedral groups 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph Wang, Dandan verfasserin aut Feng, Keqin verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfieldsSound	10.1016/j.disc.2019.111636 doi (DE-627)ELV003251683 (ELSEVIER)S0012-365X(19)30306-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Cao, Xiwang verfasserin aut Pretty good state transfer on Cayley graphs over dihedral groups 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST. Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph Wang, Dandan verfasserin aut Feng, Keqin verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
language	English
source	Enthalten in Discrete mathematics 343 volume:343
sourceStr	Enthalten in Discrete mathematics 343 volume:343
format_phy_str_mv	Article
bklname	Kombinatorik Graphentheorie Algebra: Allgemeines Mathematische Logik Mengenlehre
institution	findex.gbv.de
topic_facet	Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph
dewey-raw	510
isfreeaccess_bool	false
container_title	Discrete mathematics
authorswithroles_txt_mv	Cao, Xiwang @@aut@@ Wang, Dandan @@aut@@ Feng, Keqin @@aut@@
publishDateDaySort_date	2019-01-01T00:00:00Z
hierarchy_top_id	266882439
dewey-sort	3510
id	ELV003251683
language_de	englisch
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author	Cao, Xiwang
spellingShingle	Cao, Xiwang ddc 510 bkl 31.12 bkl 31.20 bkl 31.10 misc Perfect state transfer misc Pretty good state transfer misc Cayley graph misc Eigenvalues of a graph Pretty good state transfer on Cayley graphs over dihedral groups
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topic_title	510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Pretty good state transfer on Cayley graphs over dihedral groups Perfect state transfer Pretty good state transfer Cayley graph Eigenvalues of a graph
topic	ddc 510 bkl 31.12 bkl 31.20 bkl 31.10 misc Perfect state transfer misc Pretty good state transfer misc Cayley graph misc Eigenvalues of a graph
topic_unstemmed	ddc 510 bkl 31.12 bkl 31.20 bkl 31.10 misc Perfect state transfer misc Pretty good state transfer misc Cayley graph misc Eigenvalues of a graph
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title	Pretty good state transfer on Cayley graphs over dihedral groups
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title_full	Pretty good state transfer on Cayley graphs over dihedral groups
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title_sort	pretty good state transfer on cayley graphs over dihedral groups
title_auth	Pretty good state transfer on Cayley graphs over dihedral groups
abstract	The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST.
abstractGer	The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST.
abstract_unstemmed	The transition matrix of a graph Γ with the adjacency matrix A is defined by H ( t ) ≔ exp ( − ı t A ) , where t ∈ R and ı = − 1 . The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0 , there is a time t such that \| e v t H ( t ) e u \| ≥ 1 − ε . The state transfer is perfect if the above inequality holds for ε = 0 . Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. In this paper, we study pretty good state transfer on Cayley graphs over dihedral groups. We find that if n is a power of 2, then Cay ( D n , S ) exhibits pretty good state transfer for some subset S in D n , some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay ( D n , S ) to have PGST.
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title_short	Pretty good state transfer on Cayley graphs over dihedral groups
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score	7.401573

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Pretty good state transfer on Cayley graphs over dihedral groups

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Zugang & Verfügbarkeit

Vorhandene Bände

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