Paper Title
On A Partial Generalized Fibonacci Graph and Its Applications to Production Lines

Abstract
This paper explores the relationship between algebraic expressions and labeled graphs, focusing on a new graph type, the n-vertex partial generalized Fibonacci (PGF) graph. Our goal is to simplify the expression associated with this graph, since under the symbolic approach described in this paper, an efficient shortest-path algorithm on a graph corresponds to a shortest (or at least compact) form of its expression. To this end, we propose a decomposition method that generates an expression of polynomial length in n. In addition, we consider a production line structured as a PGF graph and scheduled by an algorithm embedded in the graph expression. Keywords - Generalized Fibonacci graph, Expression, Decomposition, Shortest path, Production line.