Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory

Abstract

In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a bipartite graph $\overline{B_{\Lambda }}$ and we classify all such algebras $\Lambda$ for which $\overline{B_{\Lambda }}$ is regular or edge-transitive. We also show that if $\overline{B_{\Lambda }}$ is semi-regular, then it is a reflexive graph.

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