Additive functions on quivers
An integral function on the set of vertices of a graph is additive if twice its value at any vertex \(v\) equals the sum of its values at all adjacent vertices, counting multiple edges, or equivalently, if the function is an eigenvector of a graph with eigenvalue 2. The authors study integral functions on finite quivers, i.e. finite oriented graphs without oriented cycles, relating the concept of additivity to the radical of the homological Euler form, and discuss the existence and constructions of their additive functions.
scientific article; zbMATH DE number 1915496