Fibonacci Graphs and their Expressions

TL;DR

This paper explores Fibonacci graphs, focusing on simplifying their algebraic expressions and finding the shortest representations, to better understand their structure and expression generation methods.

Contribution

It introduces methods for generating Fibonacci graph expressions and compares their effectiveness in simplifying these expressions.

Findings

Multiple methods for expression generation are analyzed.

Simplification techniques reduce expression complexity.

The shortest expression representations are identified.

Abstract

The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the expressions of Fibonacci graphs and eventually find their shortest representations. With that end in view, we describe the number of methods for generating Fibonacci graph expressions and carry out their comparative analysis.