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.
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The author is deeply grateful to the referee for careful reading of the article and for the valuable suggestions which greatly improved the manuscript.
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Benkhalifa, M. Rational homotopy theory methods in graph theory. AAECC 34, 603–618 (2023). https://doi.org/10.1007/s00200-021-00522-7
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DOI: https://doi.org/10.1007/s00200-021-00522-7