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Fibonacci and Telephone Numbers in Extremal Trees

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Bednarz U., Włoch I.

Discussiones Mathematicae Graph Theory

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2017

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tom 38

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nr 1

121-133

EN

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.

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Distance Fibonacci numbers, their interpretations and matrix generators

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Bednarz U., Wołowiec-Musiał M.

Commentationes Mathematicae

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2013

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tom 53

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nr 1

EN

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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Note about sequences of extrema \((A,2B)\)-edge coloured trees

100%

Bednarz U., Włoch I.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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2017

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tom 71

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nr 2

EN

In this paper we determine successive extremal trees with respect to the number of all \((A,2B)\)-edge colourings.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Commentationes Mathematicae

1 Discussiones Mathematicae Graph Theory

3 Bednarz U.

2 Włoch I.

1 Wołowiec-Musiał M.

1 2018

1 2017

1 2013

Fibonacci and Telephone Numbers in Extremal Trees

Distance Fibonacci numbers, their interpretations and matrix generators

Note about sequences of extrema \((A,2B)\)-edge coloured trees