Skip to main content
Top
Published in: Applicable Algebra in Engineering, Communication and Computing 4/2023

21-08-2021 | Original Paper

Rational homotopy theory methods in graph theory

Author: Mahmoud Benkhalifa

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between graph theory and rational homotopy theory, this paper defines new algebraic invariants for a non-oriented, simple, connected and finite graph G namely the rational cohomology \(H^*(G)\), the Lusternik-Schnirelmann category cat(G), the cohomology Euler-Poincaré characteristic \(\chi _G\), the Koszul-Poincare series \({{\mathcal {U}}}_{G}(z)\) and the formal dimension fd(G). Moreover we compute those invariants by exploiting some deep well known theorems from rational homotopy theory.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Literature
1.
go back to reference Benkhalifa, M.: Realisabitity of the group of selh-homotopy equivalences and local homotopy theory, to appear in Homology, Homotopy and Applications Benkhalifa, M.: Realisabitity of the group of selh-homotopy equivalences and local homotopy theory, to appear in Homology, Homotopy and Applications
3.
4.
go back to reference Benkhalifa, M.: The Adams-Hilton Model and the group of self-homotopy equivalences of simply connected CW-Complex. Homol. Homotopy Appl. 21(2), 345–362 (2019)MathSciNetCrossRefMATH Benkhalifa, M.: The Adams-Hilton Model and the group of self-homotopy equivalences of simply connected CW-Complex. Homol. Homotopy Appl. 21(2), 345–362 (2019)MathSciNetCrossRefMATH
5.
go back to reference Benkhalifa, M., Smith, S.B.: The effect of cell attachment on the group of self-equivalences of an R-local space. J. Homotopy Relat. Struct. 10(3), 549–564 (2015)MathSciNetCrossRefMATH Benkhalifa, M., Smith, S.B.: The effect of cell attachment on the group of self-equivalences of an R-local space. J. Homotopy Relat. Struct. 10(3), 549–564 (2015)MathSciNetCrossRefMATH
6.
go back to reference Félix, Y., Halperin, S., Thomas, J.-C.: Rational homotopy theory, Graduate Texts in Mathematics, vol. 205. Springer-Verlag, New York (2001)CrossRef Félix, Y., Halperin, S., Thomas, J.-C.: Rational homotopy theory, Graduate Texts in Mathematics, vol. 205. Springer-Verlag, New York (2001)CrossRef
7.
go back to reference Hilali, M.R.: Action du tore \(T_n\) sur les espaces simplement connexes. PhD thesis, Universite catholique de Louvain, (1980) Hilali, M.R.: Action du tore \(T_n\) sur les espaces simplement connexes. PhD thesis, Universite catholique de Louvain, (1980)
9.
go back to reference Lupton, G.: The rational toomer invariant and certain elliptic spaces, contemporary mathematics. Am. Math. Soc 316, 135–146 (2002)MATH Lupton, G.: The rational toomer invariant and certain elliptic spaces, contemporary mathematics. Am. Math. Soc 316, 135–146 (2002)MATH
Metadata
Title
Rational homotopy theory methods in graph theory
Author
Mahmoud Benkhalifa
Publication date
21-08-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 4/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00522-7

Other articles of this Issue 4/2023

Applicable Algebra in Engineering, Communication and Computing 4/2023 Go to the issue

Premium Partner