Ali F. H. The Laplace Transform as a Graph-Based Data Structure

Abstract

In this paper, we present a graph-based structural reformulation of the Laplace transform, referred to as the Laplace Transform Graph (LTG). Within this framework, functions in the time and frequency domains are treated as structured data objects (vertices), while directed edges represent direct and inverse Laplace transform operators.

The LTG provides a unified two-layer mapping structure between functional spaces, explicitly linking each function to its transformed counterpart. The proposed model establishes formal structural properties, including cycle formation, vertex degree characteristics, and convergence constraints induced by transformation consistency.

Computational algorithms are developed to construct and analyze the LTG, enabling path simplification and structural verification. The framework offers a data-oriented perspective on the Laplace transform, bridging functional analysis and graph-based structural modeling for both theoretical interpretation and computational implementation.