Isomorphism criterion for monomial graphs
Let q be a prime power, 𝔽q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over 𝔽q, with two vertices (p1, p2) ∈ P and [ l1, l2] ∈ L being adjacent i...
Saved in:
| Published in | Journal of graph theory Vol. 48; no. 4; pp. 322 - 328 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.04.2005
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Let q be a prime power, 𝔽q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over 𝔽q, with two vertices (p1, p2) ∈ P and [ l1, l2] ∈ L being adjacent if and only if p2 + l2 = p 1kl 1m. We prove that graphs Gq(k, m) and Gq′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q − 1), gcd (m, q − 1)} = {gcd (k′, q − 1),gcd (m′, q − 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005 |
|---|---|
| AbstractList | Let q be a prime power, 𝔽q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over 𝔽q, with two vertices (p1, p2) ∈ P and [ l1, l2] ∈ L being adjacent if and only if p2 + l2 = p 1kl 1m. We prove that graphs Gq(k, m) and Gq′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q − 1), gcd (m, q − 1)} = {gcd (k′, q − 1),gcd (m′, q − 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005 Abstract Let q be a prime power, q be the field of q elements, and k , m be positive integers. A bipartite graph G = G q ( k , m ) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over q , with two vertices ( p 1 , p 2 ) ∈ P and [ l 1 , l 2 ] ∈ L being adjacent if and only if p 2 + l 2 = p l . We prove that graphs G q ( k , m ) and G q ′ ( k ′, m ′) are isomorphic if and only if q = q ′ and {gcd ( k , q − 1), gcd ( m , q − 1)} = {gcd ( k ′, q − 1),gcd ( m ′, q − 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005 |
| Author | Viglione, Raymond Dmytrenko, Vasyl Lazebnik, Felix |
| Author_xml | – sequence: 1 givenname: Vasyl surname: Dmytrenko fullname: Dmytrenko, Vasyl email: dmytrenk@math.udel.edu organization: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716 – sequence: 2 givenname: Felix surname: Lazebnik fullname: Lazebnik, Felix email: lazebnik@math.udel.edu organization: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716 – sequence: 3 givenname: Raymond surname: Viglione fullname: Viglione, Raymond email: rviglion@kean.edu organization: Department of Mathematics and Computer Science, Kean University, Union, New Jersey 07083 |
| BookMark | eNp1j09PwjAYhxuDiQM9-A125TB4265_djREJkLUA4Zj020dFNlKWhLl2zudevP0Jm-e55c8QzRoXWsQusUwwQBkut-eJgSAsQsUYchEAhjLAYqA8jTJgKRXaBjCHro3Axmh8SK4xvnjzoYmLr09GW9dG9fOx41rXWP1Id56fdyFa3RZ60MwNz93hF7n9-vZQ7J6zhezu1VSUhAsqajmMmUMuDC0EkxCmZU8zViRZVwIXGBRcCkJrXElsJGCUTCEaGKo4bjmdITG_W7pXQje1OrobaP9WWFQX42qa1TfjR077dl3ezDn_0H1mK9_jaQ3bDiZjz9D-zfFBRVMbZ5yJQVZLjf5XL3QT1m-YhM |
| CitedBy_id | crossref_primary_10_1080_0025570X_2019_1614820 crossref_primary_10_1016_j_disc_2014_07_004 crossref_primary_10_1142_S0219265917410067 crossref_primary_10_1016_j_ffa_2006_03_001 |
| Cites_doi | 10.1002/jgt.10064 10.1007/978-1-4757-2103-4 10.1002/jgt.1024 10.1006/aama.2001.0794 10.1090/S0025-5718-03-01612-0 |
| ContentType | Journal Article |
| Copyright | Copyright © 2005 Wiley Periodicals, Inc. |
| Copyright_xml | – notice: Copyright © 2005 Wiley Periodicals, Inc. |
| DBID | BSCLL AAYXX CITATION |
| DOI | 10.1002/jgt.20055 |
| DatabaseName | Istex CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1097-0118 |
| EndPage | 328 |
| ExternalDocumentID | 10_1002_jgt_20055 JGT20055 ark_67375_WNG_872KKWGF_P |
| Genre | article |
| GroupedDBID | -DZ -~X .3N .GA .Y3 05W 0R~ 10A 186 1L6 1OB 1OC 1ZS 3-9 31~ 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 6TJ 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AANLZ AAONW AASGY AAXRX AAZKR ABCQN ABCUV ABDBF ABDPE ABEML ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCFJ ACCZN ACGFO ACGFS ACIWK ACNCT ACPOU ACSCC ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN AEEZP AEGXH AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFZJQ AHBTC AI. AIAGR AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN AMBMR AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE FSPIC G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ H~9 IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6L MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MVM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RX1 SAMSI SUPJJ TN5 UB1 UPT V2E V8K VH1 VJK VQA W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WRC WWM WXSBR WYISQ XBAML XG1 XJT XPP XV2 XXG YQT ZZTAW ~IA ~WT G8K AAYXX CITATION |
| ID | FETCH-LOGICAL-c3075-d3a68455067e3d7580c9c6495b996771b17b68823f1d71e87530e22a2e3e61f63 |
| IEDL.DBID | DR2 |
| ISSN | 0364-9024 |
| IngestDate | Fri Aug 23 01:15:42 EDT 2024 Sat Aug 24 01:02:47 EDT 2024 Wed Oct 30 10:04:49 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c3075-d3a68455067e3d7580c9c6495b996771b17b68823f1d71e87530e22a2e3e61f63 |
| Notes | ark:/67375/WNG-872KKWGF-P istex:C2C5E230F4A7029161B4AA24AE7DDCFE1A5826EE ArticleID:JGT20055 |
| PageCount | 7 |
| ParticipantIDs | crossref_primary_10_1002_jgt_20055 wiley_primary_10_1002_jgt_20055_JGT20055 istex_primary_ark_67375_WNG_872KKWGF_P |
| PublicationCentury | 2000 |
| PublicationDate | April 2005 |
| PublicationDateYYYYMMDD | 2005-04-01 |
| PublicationDate_xml | – month: 04 year: 2005 text: April 2005 |
| PublicationDecade | 2000 |
| PublicationPlace | Hoboken |
| PublicationPlace_xml | – name: Hoboken |
| PublicationTitle | Journal of graph theory |
| PublicationTitleAlternate | J. Graph Theory |
| PublicationYear | 2005 |
| Publisher | Wiley Subscription Services, Inc., A Wiley Company |
| Publisher_xml | – name: Wiley Subscription Services, Inc., A Wiley Company |
| References | K. Ireland and M. Rosen, A classical introduction to modern number theory, Second edition, Graduate texts in mathematics, vol. 84, Springer-Verlag, New York, 1990. F. Lazebnik and D. Mubayi, New lower bounds for Ramsey numbers of graphs and hypergraphs, Adv Appl Math 28 (3/4) (2002), 544-559. F. Lazebnik and R. Viglione, An infinite series of regular edge- but not vertex-transitive graphs, J Graph Theory 41 (2002), 249-258. F. Lazebnik and A. Thomason, Orthomorphisms and the construction of projective planes, Math Comput 73 (247) (2004), 1547-1557. F. Lazebnik and J. Verstraëte, On hypergraphs of girth five, Electron J Combin 10 (R25) (2003), 1-15. F. Lazebnik and A. J. Woldar, General properties of some families of graphs defined by systems of equations, J Graph Theory 38 (2001), 65-86. 1990; 84 2002; 28 2004; 73 2001; 38 2002 2002; 41 2003; 10 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 Lazebnik F. (e_1_2_1_6_2) 2003; 10 e_1_2_1_3_2 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – volume: 84 year: 1990 – volume: 38 start-page: 65 year: 2001 end-page: 86 article-title: General properties of some families of graphs defined by systems of equations publication-title: J Graph Theory – volume: 10 start-page: 1 issue: R25 year: 2003 end-page: 15 article-title: On hypergraphs of girth five publication-title: Electron J Combin – volume: 41 start-page: 249 year: 2002 end-page: 258 article-title: An infinite series of regular edge‐ but not vertex‐transitive graphs publication-title: J Graph Theory – year: 2002 – volume: 73 start-page: 1547 issue: 247 year: 2004 end-page: 1557 article-title: Orthomorphisms and the construction of projective planes publication-title: Math Comput – volume: 28 start-page: 544 issue: 3/4 year: 2002 end-page: 559 article-title: New lower bounds for Ramsey numbers of graphs and hypergraphs publication-title: Adv Appl Math – ident: e_1_2_1_7_2 doi: 10.1002/jgt.10064 – ident: e_1_2_1_2_2 doi: 10.1007/978-1-4757-2103-4 – ident: e_1_2_1_8_2 doi: 10.1002/jgt.1024 – ident: e_1_2_1_4_2 doi: 10.1006/aama.2001.0794 – ident: e_1_2_1_9_2 – ident: e_1_2_1_3_2 – ident: e_1_2_1_5_2 doi: 10.1090/S0025-5718-03-01612-0 – volume: 10 start-page: 1 issue: 25 year: 2003 ident: e_1_2_1_6_2 article-title: On hypergraphs of girth five publication-title: Electron J Combin contributor: fullname: Lazebnik F. |
| SSID | ssj0011508 |
| Score | 1.7520343 |
| Snippet | Let q be a prime power, 𝔽q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of... Abstract Let q be a prime power, q be the field of q elements, and k , m be positive integers. A bipartite graph G = G q ( k , m ) is defined as follows.... |
| SourceID | crossref wiley istex |
| SourceType | Aggregation Database Publisher |
| StartPage | 322 |
| SubjectTerms | algebraic constructions graph isomorphism number of complete bipartite subgraphs |
| Title | Isomorphism criterion for monomial graphs |
| URI | https://api.istex.fr/ark:/67375/WNG-872KKWGF-P/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fjgt.20055 |
| Volume | 48 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3PS8MwFMfDmBc9-Fucvygioodsa9ImLZ5E3eaGQ2RjOwghSTPRsVbWDcS_3iRdKxME8dbDS0ke-fF97XufAHCmfDdSGEkYEsqh54Uu5KEIoZCCEhEon3JL--ySVt9rD_1hCVzltTAZH6L44GZWht2vzQLnIq19Q0PfXmwqpG8KzF1MTTrX7VOBjjJCJ8j-U3ow1AdRThWqo1rRcuksWjFu_VjWqPaQaWyA57x7WW7JuDqfiar8_EFu_Gf_N8H6Qnw619ls2QIlFW-DtYeC3JrugMv7NJkk2vmv6cTRO4pBOSexo6WtM7ElzLq9hVynu6DfuOvdtODiOgUo9UL2YYQ5CUwRM6EKRzpOqMtQEh0gCR3zUOoKlwqiBTceuRF1lQlk6gohjhRWxB0RvAfKcRKrfeBoEUS90G4HkYc9yX0ZaFuCIiR43cMVcJo7lr1n1AyW8ZER0-NmdtwVcG5dXljw6dikmVGfDbpNFlDU6QyaDfZYARfWkb-_irWbPftw8HfTQ7BqMaw2C-cIlGfTuTrWAmMmTuxM-gJpTchs |
| link.rule.ids | 315,783,787,1378,27938,27939,46308,46732 |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED_m9qA--C3OzyIi-tBtTdqkBV9E3feGyMb2IqFpM9GxVdYNxL_eJN0qEwTxrQ-X0jtyd79L734BuBCOFQqMAtMj1Ddt27NM3-OeyQNOCXeFQ33N9tkm1a5d7zv9DNwsZmESfoj0wE15ho7XysHVgXTxmzX07UX3QjrOCuSku2N1f8H9U0oepaCOm_yptE1PpqIFr1AJFdOlS9kopwz7sYxSdZopb8Lz4gOT7pJhYTblheDzB3fjfzXYgo05_jRukw2zDRkx3oH1VkreGu_CdS2ORpG0_2s8MmRQUWzO0diQ6NYY6SlmuV7zXMd70C0_dO6q5vxGBTOQvuyYIfaJq-aYCRU4lKVCKfACImskLsseSi1uUU4k5sYDK6SWULVMSSDkI4EFsQYE70N2HI3FARgSB1Hb0xEhtLEd-E7gSlmCQsT9ko3zcL6wLHtPiDNYQpGMmNSbab3zcKltnkr4k6HqNKMO67UrzKWo0ehVyuwxD1fakr-_itUrHf1w-HfRM1itdlpN1qy1G0ewpllZdVPOMWSnk5k4kXhjyk_1tvoCCZPMhg |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3fS8MwEMcPnSD64G9x_iwiog-dbZImLT6JurlNh8jGfBBC02aisnWsG4h_vUlqKxME8a0PSWmO5O577d2nAEfSc2OJUWQHlIU2IYFrh4EIbBEJRoUvPRYa2meL3nRI49F7nIHzvBcm40MUL9z0yTD-Wh_wYdw7-4aGvj6bUkjPm4U5QrGj67muHgp2lFY6fvahktiBikQ5VshBZ8XUqWA0p-36Pi1STZSpLsNT_nxZcclbZTIWlejjB7rxnwtYgaUv9WldZNtlFWbkYA0W7wp0a7oOp_U06SfK-i9p31IuRbOck4GltK3VNz3Mar6hXKcb0Klety9v7K__KdiROsmeHeOQ-rqLmTKJY5UoOFEQUZUhCZX0MOYKlwmqFDfuuTFzpc5kHIlQiCSW1O1RvAmlQTKQW2ApFcRIYPxBTDCJQi_y1ViKYiRCh-AyHOaG5cMMm8EzQDLiat3crLsMx8bkxYhw9KbrzJjHu60a9xlqNru1Kr8vw4kx5O-34o1a21xs_33oAczfX1X5bb3V3IEFg2Q1FTm7UBqPJnJPiY2x2Deb6hPKess1 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Isomorphism+criterion+for+monomial+graphs&rft.jtitle=Journal+of+graph+theory&rft.au=Dmytrenko%2C+Vasyl&rft.au=Lazebnik%2C+Felix&rft.au=Viglione%2C+Raymond&rft.date=2005-04-01&rft.issn=0364-9024&rft.eissn=1097-0118&rft.volume=48&rft.issue=4&rft.spage=322&rft.epage=328&rft_id=info:doi/10.1002%2Fjgt.20055&rft.externalDBID=n%2Fa&rft.externalDocID=10_1002_jgt_20055 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0364-9024&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0364-9024&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0364-9024&client=summon |