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.

受 Lechuga 和 Murillo (Topology 39:89–94, 2000) 基础工作的启发，他们在图论和有理同伦论之间建立了联系，本文为无向、简单、连通和有限的图G定义了新的代数不变量即有理上同调\(H^*(G)\)，Lusternik-Schnirelmann 范畴猫( G )，上同调 Euler-Poincaré 特征\(\chi _G\)，Koszul-Poincare 级数\({{\mathcal {U}}}_{G}(z)\)和形式维度fd ( G )。此外，我们通过利用有理同伦理论中一些深刻的众所周知的定理来计算这些不变量。