Summary: Suppose that \(G(p, q)\) is a graph with \(p\) vertices and \(q\) edges, \((a, d)\)-vertex-antimagic total labeling (\((a, d)\)-VATL) is an bijection \(\lambda\) from \(V(G)\cup E(G)\) to the consecutive integers \((1+2, \cdots, p+q)\), where the sum of the labels of every vertex and its incident edges form an arithmetic progression with the initial term \(a\) and difference \(d\). In this project, an algorithm is designed to judge the \((a, d)\)-vertex-antimagic total labelings of nonisomorphic graphs within finite vertices. It is found that some of them don’t have \((a, 1)\)-vertex-antimagic total labelings under certain conditions, and these graphs are classified and defined. At the same time, the rules of non-\((a, d)\)-vertex antimagic are summarized, and the theorems are given.