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Fibonacci and Telephone Numbers in Extremal Trees

Urszula BednarzIwona Włoch — 2018

Discussiones Mathematicae Graph Theory

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.

Distance Fibonacci numbers, their interpretations and matrix generators

Urszula BednarzMałgorzata Wołowiec-Musiał — 2013

Commentationes Mathematicae

In this paper we define a distance Fibonacci numbers, also for negative integers, which generalize the classical Fibonacci numbers and Padovan numbers, simultaneously. We give different interpretations of these numbers with respect to special partitions and compositions, also in graphs. We show a construction of the sequence of distance Fibonacci numbers using the Pascal's triangle. Moreover, we give matrix generators of these numbers, for negative integers, too.

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