Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. Graph labelings were first introduced in the 1960's where the vertices and edges are assigned real values or subsets of a set subject to certain conditions. An enormous body of literature has grown around graph labeling in the last five decades. Labeled graphs provide mathematical models for a broad range of applications. The qualitative labelings of a graph element have been used in diverse fields such as Conflict resolutions in Social psychology, Energy crises etc. Quantitative labelings of graph elements have been used in Missile guidance codes, Radar location codes, Coding theory, X-Ray Crystallography, Radio-Astronomy, Circuit design, Communication Network and the like Most popular graph labelings trace their origin to one introduced by Rosa This thesis is devoted to the study of magic strength of several graphs, super edge-magic labeling, and super edge-magic strength of several graphs, super vertex-magic labeling, total super magic labeling and anti super edge-magic labeling and the corresponding strengths.