International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 345-348
From paths to stars
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 of a tree is known to increase
with the diameter of the tree. A similar question is raised and settled for the number of
complete subgraphs in for a special class of trees via Fibonacci numbers. A structural
characterization of extremal trees is also presented.