An overview of hypercompositional algebra applications on graphs

Abstract

Graphs are fundamental structures in mathematics and computer science for modeling relationships between objects. This paper studies three hypercompositional structures that are derived from graphs, namely the Path hyperoperation, Simple Path hyperoperation, and Ancestry hyperoperation. These hyperoperations capture complex relationships, offering a robust framework for analyzing intricate connections within graphs. We investigate their properties and provide detailed examples to illustrate their applications.