Abstract:
One of the simplest and the most useful theory in the field of mathematics is graph theory. Many authors work on it and consider it as a powerful tool in different directions, such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, data base management, secret sharing schemes, and models for constraint programming over finite domains. Let H be a graph. An edge-covering of G is a finite family of subgraphs such that each edge of G belongs to at least one of the subgraphs to a given graph H, then G admits an H-covering. Suppose G admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. The graph G is said to be H-magic if there
exists a bijection (x) : V [ E ! {1, 2, 3...|V | + |E|} such that for every subgraph h of G isomorphic to H, P (v) +P (e) is constant. if (v) = {1, 2, 3...|V |}, then G is said to be H-supermagic. A graph that admits an H-supermagic labeling is called H-supermagic graph.This dissertation studies about the H-supermagic total labeling of grid graph as well as for isomorphic copies of grid graph. We also construct the Cn-magic and super-magic labeling on Harary graph as well as isomorphic and non-isomorphic copies of Harary graphs.
This dissertation also studies about the construction of C4-supermagic labeling on ladder and prism graphs.