A Note on Algebraic Expressions of Rhomboidal Labeled Graphs

This paper investigates relationship between algebraic expressions and labeled graphs. We consider rhomboidal non-series-parallel graphs, specifically, a new digraph called a full square rhomboid. Our intent is to simplify the expressions of rhomboidal graphs and eventually find their shortest representations. With that end in view, we describe and compare two decomposition methods for generating expressions of labeled graphs.