Opuscula Math. 37, no. 4 (2017), 479-490
http://dx.doi.org/10.7494/OpMath.2017.37.4.479

 
Opuscula Mathematica

On Fibonacci numbers in edge coloured trees

Urszula Bednarz
Dorota Bród
Anetta Szynal-Liana
Iwona Włoch
Małgorzata Wołowiec-Musiał

Abstract. In this paper we show the applications of the Fibonacci numbers in edge coloured trees. We determine the second smallest number of all \((A,2B)\)-edge colourings in trees. We characterize the minimum tree achieving this second smallest value.

Keywords: edge colouring, tree, tripod, Fibonacci numbers.

Mathematics Subject Classification: 11B37, 11C20, 15B36, 05C69.

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  1. U. Bednarz, I. Włoch, M. Wołowiec-Musiał, Total graph interpretation of numbers of the Fibonacci type, J. Appl. Math. 2015 (2015), Article ID 837917.
  2. C. Berge, Principle of Combinatorics, Academic Press, New York, London, 1971.
  3. R. Diestel, Graph Theory, Springer-Verlag, Heidelberg, New York, 2005.
  4. H. Prodinger, R.F. Tichy, Fibonacci numbers of graphs, Fibonacci Quart. 20 (1982) 1, 16-21.
  • Urszula Bednarz
  • Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
  • Dorota Bród
  • Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
  • Anetta Szynal-Liana
  • Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
  • Iwona Włoch
  • Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
  • Małgorzata Wołowiec-Musiał
  • Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
  • Communicated by Gyula O.H. Katona.
  • Received: 2016-04-12.
  • Revised: 2016-09-16.
  • Accepted: 2016-09-16.
  • Published online: 2017-04-28.
Opuscula Mathematica - cover

Cite this article as:
Urszula Bednarz, Dorota Bród, Anetta Szynal-Liana, Iwona Włoch, Małgorzata Wołowiec-Musiał, On Fibonacci numbers in edge coloured trees, Opuscula Math. 37, no. 4 (2017), 479-490, http://dx.doi.org/10.7494/OpMath.2017.37.4.479

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