Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers previously on this topic. This research paper focuses on antimagic labeling of different types of graphs and trees. It entails the assignment of distinct prime values to edges in a manner that ensures the cumulative sum of edge labels at each vertex remains unique. This research proposes a conjecture on antimagic labeling of any graphs and proves two theories. Firstly, we tried to give weights to the edges randomly, as some exceptions are faced in particular phases in this way, we followed a whole new way to mitigate this problem. This research paper demonstrates computational and mathematical verification to prove that antimagic labeling of any perfect binary tree and complete graph is possible.

翻译：图标号是一种为图顶点或边分配唯一标号或权重的技术，常用于分析与解决各类图相关的问题。此前已有研究者就此课题提出若干方法，但存在一定局限性。本文聚焦于不同类型图与树的**反魔法标号**（antimagic labeling），即需为每条边赋予不同的素数，使得每个顶点所关联的边标号之和保持唯一性。本研究针对任意图的反魔法标号问题提出一个猜想，并证明两个定理。首先，我们尝试对边随机赋权，但在特定阶段遇到若干例外情况，为此我们采用全新方法予以应对。本文通过计算验证与数学证明，论证了任意完美二叉树与完全图的反魔法标号均可行。