Abstract: A subcubic graph refers to a simple connected graph with a maximum degree of no more than 3. A normal subcubic graph is a subcubic graph with a minimum degree of at least 2, meaning that the degree of any vertex in the graph ranges between 2 and 3. A D(2)- vertex sum distinguishing edge coloring of a graph is a proper edge coloring such that for any two vertices \mathrmu and \mathrmv with a distance of no more than 2 in the graph, the sums of the colors of the edges incident to them are different.In this paper, by analyzing the structural characteristics of subcubic graphs, the method of proof by contradiction and the principle of minimal counterexamples are employed. Specifically, it is assumed that there exists a minimal counterexample that does not possess a certain minimal property. Then, a contradiction is derived, demonstrating the existence of such a minimal counterexample. Subsequently, another contradiction arises from the overall assertion, thereby proving the validity of the theorem. Combining the Zero-One Polynomial Theorem, which utilizes algebraic tools to analyze the quantitative relationships among elements within the structure, the structural characteristics of subcubic graphs are revealed from multiple dimensions. This paper discusses the D(2)- vertex sum distinguishing edge coloring problem of subcubic graphs and concludes that their D(2)- vertex sum distinguishing edge chromatic number does not exceed 12, providing new theoretical achievements and practical references for the study of graph coloring theory in graph theory.