Skip to main content
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2017

21.07.2016 | Original Research

On topological properties of hierarchical interconnection networks

verfasst von: Haidar Ali, A. Q. Baig, Muhammad Kashif Shafiq

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

There is really a lot of mathematics involved in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. A lot of computers linked together form a network. Cell phone users form a network. Networking involves the study of the best way of implementing a network. Graph theory has found a considerable use in this area of research. In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randić index \(R_{\alpha }(G)\) for different values of “\(\alpha \)” for block shift network (BSN-1) and (BSN-2), Hierarchical hypercube (HHC-1) and (HHC-2). We also compute first Zagreb, \(\textit{ABC}\), \(\textit{GA}\), \(\textit{ABC}_{4}\) and \(\textit{GA}_{5}\) indices and give closed formulae of these indices for Hierarchical interconnection networks.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Abd-El-Barr, M., Al-Somani, T.F.: Topological properties of hierarchical interconnection networks: a review and comparison. J. Electr. Comput. Eng. (2011). doi:10.1155/2011/189434 Abd-El-Barr, M., Al-Somani, T.F.: Topological properties of hierarchical interconnection networks: a review and comparison. J. Electr. Comput. Eng. (2011). doi:10.​1155/​2011/​189434
2.
Zurück zum Zitat Bača, M., Horváthová, J., Mokrišová, M., Suhányiovǎ, A.: On topological indices of fullerenes. Appl. Math. Comput. 251, 154–161 (2015)MathSciNetMATH Bača, M., Horváthová, J., Mokrišová, M., Suhányiovǎ, A.: On topological indices of fullerenes. Appl. Math. Comput. 251, 154–161 (2015)MathSciNetMATH
3.
Zurück zum Zitat Baig, A.Q., Imran, M., Ali, H.: Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 9, 248–255 (2015) Baig, A.Q., Imran, M., Ali, H.: Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 9, 248–255 (2015)
4.
Zurück zum Zitat Baig, A.Q., Imran, M., Ali, H.: On topological indices of poly oxide, poly silicate, DOX and DSL networks. Can. J. Chem. 93, 730739 (2015)CrossRef Baig, A.Q., Imran, M., Ali, H.: On topological indices of poly oxide, poly silicate, DOX and DSL networks. Can. J. Chem. 93, 730739 (2015)CrossRef
5.
Zurück zum Zitat Diudea, M.V., Gutman, I., Lorentz, J.: Molecular Topology. Nova, Huntington (2001) Diudea, M.V., Gutman, I., Lorentz, J.: Molecular Topology. Nova, Huntington (2001)
6.
Zurück zum Zitat Estrada, E., Torres, L., Rodríguez, L., Gutman, I.: An atom–bond connectivity index: modelling the enthalpy of formation of alkanes. Indian J. Chem. 37A, 849–855 (1998) Estrada, E., Torres, L., Rodríguez, L., Gutman, I.: An atom–bond connectivity index: modelling the enthalpy of formation of alkanes. Indian J. Chem. 37A, 849–855 (1998)
7.
Zurück zum Zitat Ghorbani, M., Hosseinzadeh, M.A.: Computing \(ABC_{4}\) index of nanostar dendrimers. Optoelectron. Adv. Mater. Rapid Commun. 4, 1419–1422 (2010) Ghorbani, M., Hosseinzadeh, M.A.: Computing \(ABC_{4}\) index of nanostar dendrimers. Optoelectron. Adv. Mater. Rapid Commun. 4, 1419–1422 (2010)
8.
Zurück zum Zitat Graovac, A., Ghorbani, M., Hosseinzadeh, M.A.: Computing fifth geometric–arithmetic index for nanostar dendrimers. J. Math. Nanosci. 1, 3342 (2011) Graovac, A., Ghorbani, M., Hosseinzadeh, M.A.: Computing fifth geometric–arithmetic index for nanostar dendrimers. J. Math. Nanosci. 1, 3342 (2011)
9.
Zurück zum Zitat Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry. Springer, New York (1986)CrossRefMATH Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry. Springer, New York (1986)CrossRefMATH
10.
Zurück zum Zitat Hayat, S., Imran, M.: Computation of topological indices of certain networks. Appl. Math. Comput. 240, 213–228 (2014)MathSciNetMATH Hayat, S., Imran, M.: Computation of topological indices of certain networks. Appl. Math. Comput. 240, 213–228 (2014)MathSciNetMATH
11.
Zurück zum Zitat Hayat, S., Imran, M.: Computation of certain topological indices of nanotubes. J. Comput. Theor. Nanosci. 12, 70–76 (2015)CrossRef Hayat, S., Imran, M.: Computation of certain topological indices of nanotubes. J. Comput. Theor. Nanosci. 12, 70–76 (2015)CrossRef
12.
Zurück zum Zitat Hayat, S., Imran, M.: Computation of certain topological indices of nanotubes covered by \(C_{5}\) and \(C_{7}\). J. Comput. Theor. Nanosci. 12, 533–541 (2015)CrossRef Hayat, S., Imran, M.: Computation of certain topological indices of nanotubes covered by \(C_{5}\) and \(C_{7}\). J. Comput. Theor. Nanosci. 12, 533–541 (2015)CrossRef
13.
Zurück zum Zitat Hayat, S., Imran, M.: On some degree based topological indices of certain nanotubes. J. Comput. Theor. Nanosci. 12, 1599–1605 (2015)CrossRef Hayat, S., Imran, M.: On some degree based topological indices of certain nanotubes. J. Comput. Theor. Nanosci. 12, 1599–1605 (2015)CrossRef
14.
Zurück zum Zitat Huiqing, L.I.U., Zheng, Y.A.N., Heguo, L.I.U.: Extremal chemical (n, m, k)-graphs with maximum Randić index. MATCH Commun. Math. Comput. Chem. 60, 513–522 (2008)MathSciNetMATH Huiqing, L.I.U., Zheng, Y.A.N., Heguo, L.I.U.: Extremal chemical (n, m, k)-graphs with maximum Randić index. MATCH Commun. Math. Comput. Chem. 60, 513–522 (2008)MathSciNetMATH
15.
Zurück zum Zitat Iranmanesh, A., Zeraatkar, M.: Computing GA index for some nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 4, 1852–1855 (2010) Iranmanesh, A., Zeraatkar, M.: Computing GA index for some nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 4, 1852–1855 (2010)
16.
Zurück zum Zitat Konstantinidou, S.: The selective extra stage butterfly. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 1, 502–506 (1992) Konstantinidou, S.: The selective extra stage butterfly. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 1, 502–506 (1992)
17.
Zurück zum Zitat Manuel, P.D., Abd-El-Barr, M.I., Rajasingh, I., Rajan, B.: An efficient representation of Benes networks and its applications. J. Discret. Algorithms 6, 11–19 (2008)MathSciNetCrossRefMATH Manuel, P.D., Abd-El-Barr, M.I., Rajasingh, I., Rajan, B.: An efficient representation of Benes networks and its applications. J. Discret. Algorithms 6, 11–19 (2008)MathSciNetCrossRefMATH
18.
Zurück zum Zitat Othmer, H.G.: A Graph-Theoretic Analysis of Chemical Reaction Networks. University of Utah, Salt Lake City (1981) Othmer, H.G.: A Graph-Theoretic Analysis of Chemical Reaction Networks. University of Utah, Salt Lake City (1981)
19.
Zurück zum Zitat Randić, M.: On characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975)CrossRef Randić, M.: On characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975)CrossRef
20.
Zurück zum Zitat Vukičević, D., Furtula, B.: Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem. 46, 1369–1376 (2009)MathSciNetCrossRefMATH Vukičević, D., Furtula, B.: Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem. 46, 1369–1376 (2009)MathSciNetCrossRefMATH
Metadaten
Titel
On topological properties of hierarchical interconnection networks
verfasst von
Haidar Ali
A. Q. Baig
Muhammad Kashif Shafiq
Publikationsdatum
21.07.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-016-1038-3

Weitere Artikel der Ausgabe 1-2/2017

Journal of Applied Mathematics and Computing 1-2/2017 Zur Ausgabe