On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs
type: Item
instance of: scholarly article
title: On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs
zbMATH Open document ID: 0543.05037
DOI: 10.1155/S0161171283000617
author: E. J. Farrell
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45380
review text: 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.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 3863234
zbMATH Keywords: path cover
zbMATH Keywords: path polynomial
zbMATH Keywords: spanning subgraph
MaRDI profile type: Publication
OpenAlex ID: W2155723899
description: scientific article; zbMATH DE number 3863234