Fibonacci and Telephone Numbers in Extremal Trees

Abstract

In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.

Keywords

• edge colouring
• tripod
• fibonacci numbers
• telephone numbers
• 11b37
• 11c20
• 15b36
• 05c69