Abstract:

The graph G represents an undirected, simple, finite graph. G's total labeling is a bijection between its vertex and edge sets and the set {1, 2,..., p+q}, where p and q describe the cardinality of G's vertex and edge sets, respectively. In this paper, we explore the concept of Super Vertex Perfectly Total Antimagic (SVPTAT) labeling in the context of graph theory, specifically focusing on complete graphs and complete bipartite graphs K_{m,n}. We present the conditions for graphs that do not confess vertex-magic and edge-antimagic at the same time. For any n \geq 2, the Corona product of any graph with mK_1 and mK_2 does not accept vertex-magic and edge-antimagic totals concurrently. Finally, we suggest a couple of open problems for future research.