International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 321-338

Matchings in hexagonal cacti

E. J. Farrell

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

Received 21 June 1983; Revised 18 July 1986

Copyright © 1987 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 recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect-d matchings in the graphs, for various values of d. In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs.