Geodesic
Fibonacci and Telephone Numbers in Extremal Trees
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 121-133

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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 
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Bednarz, Urszula; Włoch, Iwona. Fibonacci and Telephone Numbers in Extremal Trees. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 121-133. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a9/