International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 65-73

On coefficients of path polynomials

E. J. Farrell

Department of Mathematics, The University of the West Indies, West Indies, St. Augustine, Trinidad and Tobago

Received 1 March 1982; Revised 20 December 1982

Copyright © 1984 E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.