International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 345-348
doi:10.1155/S0161171291000418
From paths to stars
A.F. Alameddine
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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.