On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs
A path cover of a graph G is a spanning subgraph with maximum degree two (that is, each component of a path cover is a, possibly trivial, path). Path polynomials are defined (akin to ''chromatic polynomials''). For example, the simple path polynomial of G is \(A_ 1w^ 1+A_ 2w^ 2+A_ 3w^ 3+...+A_ rw^ r+...\) where \(A_ r\) is the number of path covers with exactly r components. Some introductory results concerning this interesting topic are presented.
scientific article; zbMATH DE number 3863234