Group vertex magicness of H-join and generalised friendship graph

In this paper, we consider A -vertex magic graphs, where A is a non-trivial Abelian group. We characterize Z -vertex magic graphs. We also explore the relation between the A -vertex magicness of a graph G and its reduced graph. In addition, we introduce a new type of labeling called A ′ -vertex magic labeling of graphs and characterize A -vertex magicness using A ′ -vertex magicness. We give a new procedure to embed any graph as an induced subgraph of an A -vertex magic graph and we construct infinite families of A -vertex magic graphs both of these procedure uses less number of vertices compared to the one given in (Sabeel et al. in Australas. J. Combin. 85(1) (2023), 49-60) and we also generalize some results proved in this paper. Finally we completely classify generalised friendship graph using A -vertex magicness and group vertex magicness.