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

Received 14 March 1990; Revised 13 August 1990

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.