Advances in graph labelings

A graph labeling is a mapping that assigns natural numbers to vertices and/or edges of a graph. In this thesis, we consider two types of labeling; magic and irregular labeling. In both labelings, we label both vertices and edges of the graph. This type of labeling is called total labeling. In irregular labeling we can repeat some numbers in the graph, but the weights of every graph element are pairwise distinct. A graph is called H-supermagic if the weight of every subgraph H of the graph is constant. In magic labeling, we prove that banana tree, firecracker, flower and grid graph are H-supermagic. Banana tree graph is an amalgamation of connected graphs. Therefore result for banana trees is an immediate consequence of a theorem about amalgamations of connected graphs from Maryati et al. The result for firecracker graph is obtained by a similar method. For flower graph, we provide results for odd order. In the grid graphs, we prove that it is H-supermagic by induction. In irregular labeling, we consider the weight of the corresponding edges. If the weight of every edge is different we called the labeling edge irregular total labeling. We prove that the grid graphs are edge irregular.