  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.
