A graph ( , ) G V E has an H -covering if every edge in Ebelongs to a subgraph of G isomorphic to H . SupposeG admits an H -covering. AnH -magic labeling is a mapping l from ( ) ( ) E G V G È onto the integers {1,2,...,| ( ) ( )|} E G V G È with the property that, for every subgraph Aof G isomorphic toH , there is a positive integer csuch that ( ) ( ) ( ) ( ) . v V A e E A A v e c ll ÎÎ = å + å =å A graph which possess such type of labeling is known as H -magic graph. Further if in a graph vertices are labeled first with smallest positive numbers, then the graph is called H -supermagic. Moreover a graph is said to be H -( , ) ad-anti magic if the magic constant for an arithmetic progression with initial value aand a common difference . d Numerous results on labeling of many families of graphs have been published. In this thesis, research work focuses on to formulate cycle 3 C -( , ) ad anti-supermagic labeling for the MultiWheels graph, supermagic labeling for isomorphic copies with its disjoint union of Multi-Wheels graph and cycle ( , ) ad-anti-supermagic labeling for Web graph. Also cycle anti-supermagic labeling for isomorphic copies with its disjoint union of ladder and triangular ladder graphs have been formulated. In addition, investigation of fan, friendship, ladder and wheel line graphs and study of the supermagic and anti-supermagic vertex-edge-face labeling of such graphs and their isomorphic copies have been carried in this thesis. An anti-supermagic labeling of the extension of cycle graphs is also formulated.Lastly the face supermagic labeling of (1,1,1) type of subdivided triangular ladder graph, subdivided 4 mC -snake graph and subdivided 4 kmC -triangular snake graph with its (1,1,...,1) and (2,2,...,2) string are also the part of this thesis.