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The paper investigates relationship between algebraic expressions and graphs.We consider a digraph called a Fibonacci graph which gives a generic example ofnon-series-parallel graphs. Our intention in this paper is to simplify theexpressions of Fibonacci graphs and eventually find their shortestrepresentations. With that end in view, we describe the number of methods forgenerating Fibonacci graph expressions and carry out their comparativeanalysis.

Fibonacci Graphs and their Expressions