International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 345-348

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

Copyright © 1991 A. F. Alameddine. 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.


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.