A One-Vertex Decomposition Algorithm for Generating Algebraic Expressions of Square Rhomboids

The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of square rhomboids and eventually find their shortest representations. With that end in view, we describe the new algorithm for generating square rhomboid expressions, which improves on our previous algorithms.