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

TL;DR

This paper introduces a new algorithm to generate simplified algebraic expressions for square rhomboid graphs, which are non-series-parallel, aiming to find their shortest representations.

Contribution

A novel one-vertex decomposition algorithm that improves upon previous methods for generating minimal algebraic expressions of square rhomboids.

Findings

The algorithm produces shorter expressions than earlier methods.

It effectively handles non-series-parallel graph structures.

The approach enhances the efficiency of algebraic expression generation.

Abstract

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.