Full Square Rhomboids and Their Algebraic Expressions

TL;DR

This paper explores algebraic expressions of full square rhomboid graphs, introducing decomposition methods to simplify and find shortest representations of their algebraic expressions, advancing understanding of non-series-parallel graphs.

Contribution

It presents two novel decomposition methods for simplifying algebraic expressions of full square rhomboids, a class of non-series-parallel graphs.

Findings

Two decomposition methods effectively generate simplified expressions.

Comparative analysis shows advantages of each method.

Results contribute to graph algebra and complexity reduction.

Abstract

The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a full square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of full square rhomboids and eventually find their shortest representations. With that end in view, we describe two decomposition methods for generating expressions of full square rhomboids and carry out their comparative analysis.