IJPAM: Volume 106, No. 1 (2016)

THE FIBONACCI NUMBERS FOR THE MOLECULAR
GRAPHS OF LINEAR PHENYLENES

Jaroslav Seibert$^1$, Libor Koudela$^2$
$^{1,2}$Institute of Mathematics and Quantitative Methods
Faculty of Economics and Administration
University of Pardubice
Studentská 84, 532 10 Pardubice, CZECH REPUBLIC


Abstract. The concept of the Fibonacci number of an undirected graph $G=(V,E)$ refers to the number of independent vertex subsets $U$ of $V$ such that no two vertices from $U$ are adjacent in $G$. In this paper the Fibonacci numbers of molecular graphs corresponding to one type of phenylenes are calculated using the decomposition formula. Investigation of the Fibonacci numbers of certain classes of graphs leads to a difference equation or systems of difference equations. The explicit formula for the Fibonacci numbers of linear phenylenes is found as a function of the number $n$ of hexagons in the phenylene.

Received: December 4, 2015

AMS Subject Classification: 92E10, 11B39, 05C90

Key Words and Phrases: molecular graph, Fibonacci number, linear phenylene, decomposition formula, difference equation

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DOI: 10.12732/ijpam.v106i1.25 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 307 - 316


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