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Chemical Graphs. XL.1 Three Relations Between the Fibonacci Sequence and the Numbers of Kekule Structures for Non-branched cata-Condensed Polycyclic Aromatic Hydrocarbons

Alexandru T . Balaban ; Department of Organic Chemistry, The Polytechnic Institute, Splaiul Independentei 313, Bucharest, Romania
loan Tomescu ; Faculty of Mathematics, The University of Bucharest, Str. Academiei' 14, Bucharest, Romania

Puni tekst: engleski pdf 5.833 Kb

str. 391-404

preuzimanja: 303



Fo·r benze.notd or non-benzenoid ca:ta1fusenes having a non-
ibranched string 01f cata-co.ndensed rings, the numbers K of
Kekule structures (perfect matching·s) can be expressed vi the recurrence relationship (1); as a coa.-ollary when each annelated
.segment has exactly two ring.s, the numbers O'f Kelm.le
structures form the Fiibonacci sequence.
Coro.nary 2 presents a second re.lationshi:p with Fiibonacci
numbers. Algebraic expressions for the number of Kekule struc-
1tures in non-brainched cata.fusenes 1n terms of hexago.n numbers
iJn each linearly condensed segment can be obtained. The
numbers of terms in .such .a,,lgebraic expressivns lead to a new
numerical triangle (Table I) which is related to Pascal's triangle,
and which pwvides a third link with the F ~bonacci
numbers expressed either by relation (7) or by the equivalent
relation (10).

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