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.
- U. Bednarz, I. Włoch, M. Wołowiec-Musiał, Total graph interpretation of numbers of the Fibonacci type, J. Appl. Math. 2015 (2015), Article ID 837917.
- C. Berge, Principle of Combinatorics, Academic Press, New York, London, 1971.
- R. Diestel, Graph Theory, Springer-Verlag, Heidelberg, New York, 2005.
- 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.
