Extremal polyomino chains of VDB topological indices
ABSTRACT: We show that the zig-zag chain Z 3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {ϕij} under which the zig-zag chain Z 3 n is an extremal value of the induced topological index...
- Autores:
-
Cruz Rodes, Roberto
Rada Rincón, Juan Pablo
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2015
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/26796
- Acceso en línea:
- http://hdl.handle.net/10495/26796
- Palabra clave:
- Extreme values
Valores extremos
http://aims.fao.org/aos/agrovoc/c_8e611af8
Topological indices
Polyomino chains
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
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| dc.title.spa.fl_str_mv |
Extremal polyomino chains of VDB topological indices |
| title |
Extremal polyomino chains of VDB topological indices |
| spellingShingle |
Extremal polyomino chains of VDB topological indices Extreme values Valores extremos http://aims.fao.org/aos/agrovoc/c_8e611af8 Topological indices Polyomino chains |
| title_short |
Extremal polyomino chains of VDB topological indices |
| title_full |
Extremal polyomino chains of VDB topological indices |
| title_fullStr |
Extremal polyomino chains of VDB topological indices |
| title_full_unstemmed |
Extremal polyomino chains of VDB topological indices |
| title_sort |
Extremal polyomino chains of VDB topological indices |
| dc.creator.fl_str_mv |
Cruz Rodes, Roberto Rada Rincón, Juan Pablo |
| dc.contributor.author.none.fl_str_mv |
Cruz Rodes, Roberto Rada Rincón, Juan Pablo |
| dc.subject.agrovoc.none.fl_str_mv |
Extreme values Valores extremos http://aims.fao.org/aos/agrovoc/c_8e611af8 |
| topic |
Extreme values Valores extremos http://aims.fao.org/aos/agrovoc/c_8e611af8 Topological indices Polyomino chains |
| dc.subject.proposal.spa.fl_str_mv |
Topological indices Polyomino chains |
| description |
ABSTRACT: We show that the zig-zag chain Z 3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {ϕij} under which the zig-zag chain Z 3 n is an extremal value of the induced topological index T defined by T (G) = X 1≤i≤j≤n−1 mijϕij where G is a graph with n vertices and mij is the number of edges of G with terminal vertices of degree i and j. We also find extremal values of the general Randi´c index Rα over the set of all polyomino chains, for some values of α. |
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2015 |
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2015 |
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2022-03-22T21:44:04Z |
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2022-03-22T21:44:04Z |
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info:eu-repo/semantics/article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Artículo de investigación |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Cruz, R., & Rada, J. (2015). Extremal polyomino chains of VDB topological indices. Appl. Math. Sci, 9, 5371-5388. http://dx.doi.org/10.12988/ams.2015.54368 |
| dc.identifier.issn.none.fl_str_mv |
1312-885X |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10495/26796 |
| dc.identifier.doi.none.fl_str_mv |
10.12988/ams.2015.54368 |
| dc.identifier.eissn.none.fl_str_mv |
1314-7552 |
| identifier_str_mv |
Cruz, R., & Rada, J. (2015). Extremal polyomino chains of VDB topological indices. Appl. Math. Sci, 9, 5371-5388. http://dx.doi.org/10.12988/ams.2015.54368 1312-885X 10.12988/ams.2015.54368 1314-7552 |
| url |
http://hdl.handle.net/10495/26796 |
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eng |
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eng |
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Appl. Math. Sci. |
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info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/2.5/co/ |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/co/ http://purl.org/coar/access_right/c_abf2 https://creativecommons.org/licenses/by/4.0/ |
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Hikari |
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Álgebra U de A |
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Bulgaria |
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Universidad de Antioquia |
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Cruz Rodes, RobertoRada Rincón, Juan Pablo2022-03-22T21:44:04Z2022-03-22T21:44:04Z2015Cruz, R., & Rada, J. (2015). Extremal polyomino chains of VDB topological indices. Appl. Math. Sci, 9, 5371-5388. http://dx.doi.org/10.12988/ams.2015.543681312-885Xhttp://hdl.handle.net/10495/2679610.12988/ams.2015.543681314-7552ABSTRACT: We show that the zig-zag chain Z 3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {ϕij} under which the zig-zag chain Z 3 n is an extremal value of the induced topological index T defined by T (G) = X 1≤i≤j≤n−1 mijϕij where G is a graph with n vertices and mij is the number of edges of G with terminal vertices of degree i and j. We also find extremal values of the general Randi´c index Rα over the set of all polyomino chains, for some values of α.COL008689618application/pdfengHikariÁlgebra U de ABulgariainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Extremal polyomino chains of VDB topological indicesExtreme valuesValores extremoshttp://aims.fao.org/aos/agrovoc/c_8e611af8Topological indicesPolyomino chainsAppl. Math. Sci.Applied Mathematical Sciences537153888108ORIGINALCruzRoberto_2015_ExtremalPolyominoVDB.pdfCruzRoberto_2015_ExtremalPolyominoVDB.pdfArtículo de investigaciónapplication/pdf300783http://bibliotecadigital.udea.edu.co/bitstream/10495/26796/1/CruzRoberto_2015_ExtremalPolyominoVDB.pdf0843de113937347f8e2e93c122d09fb4MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927http://bibliotecadigital.udea.edu.co/bitstream/10495/26796/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/26796/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/26796oai:bibliotecadigital.udea.edu.co:10495/267962022-03-22 16:44:05.05Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |