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Erschienen in:
21.08.2021 | Original Paper
Rational homotopy theory methods in graph theory
Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 4/2023
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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.
