The number of cycles in the complement <mml:math alttext="${T'}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>T</mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:math> of a tree <mml:math alttext="$T$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> is known to increase
with the diameter of the tree. A similar question is raised and settled for the number of
complete subgraphs in <mml:math alttext="${T'}$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>T</mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:math> for a special class of trees via Fibonacci numbers. A structural
characterization of extremal trees is also presented.

International Journal of Mathematics and Mathematical Sciences

From paths to stars

Abstract

Copyright