Construction of Magic and Anti-magic Graphs

Abstract

Construction of Magic and Anti-magic Graphs An undirected graph G is said to be simple if it has no multi-edges and self-loops. If G is connected and has no cycles, it is called a tree. A labeling of a graph is a mapping that assigns usually positive integers to the vertices and edges. If a labeling uses the vertex-set or the edge-set only, then it becomes a vertex-labeling or the edge-labeling, respectively. A labeling is called total if the domain consists of both vertex and edge sets. There are many types of graph labelings already studied in the literature but in this thesis our main focus is on magic and antimagic graph labelings. We study the existence of super edge magic and super (a, d)-edge-antimagic total labeling of generalized subclasses of trees like subdivided stars, disjoint union of isomorphic copies of subdivided stars, subdivided caterpillars, generalized extended w-trees and disjoint union of isomorphic as well as non-isomorphic copies of generalized extended w-trees. It is well-reputed respected problem to study the existence of magic type and antimagic type labeling of trees and forests due to the famous Rosa-type conjectures which are still open in general sense and challenging for researchers due to their mathematical insight.