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/
| Summary: | 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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