On a Question of Prime Labeling of Graphs

In the field of graph theory, the complete graph of vertices is a simple undirected graph such that every pair of distinct vertices is connected by a unique edge. In the present work, we introduce planar subgraph of with maximal number of edges . Generally, does not admit prime labeling. We present an algorithm to obtain prime-labeled subgraphs of . We conclude the paper by stating two conjectures based on labeling of . In particular, the planar subgraph admits anti-magic labeling but does not admit edge magic total labeling.