On coefficients of path polynomials

Abstract

Explicit formulae, in terms of sugraphs of the graph, are given for the first six coefficients of the simple path polynomial of a graph. From these, explicit formulae are deduced for the number of hamiltonian paths in graphs with up to six nodes. Also simplified expressions are given for the number of ways of covering the nodes of some families of graphs with k paths, for certain values of k.

Keywords

• path polynomials
• simple path polynomials
• hamiltonian path
• path cover.