H-Supermagic Labeling of cycle like graphs

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.