Group vertex magicness of H-join and generalised friendship graph

Balamoorthy, S. (Central University of Tamil Nadu, Thiruvarur, India.)
Bharanedhar, S.V. (Central University of Tamil Nadu, Thiruvarur, India.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications

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.