Antimagic Labeling of Graphs Using Prime Numbers

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.