International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 345-348
doi:10.1155/S0161171291000418
Abstract
The number of cycles in the complement T′ of a tree T is known to increase
with the diameter of the tree. A similar question is raised and settled for the number of
complete subgraphs in T′ for a special class of trees via Fibonacci numbers. A structural
characterization of extremal trees is also presented.