On Distance Antimagic Labeling of Graphs and their Products

Abstract

In graph theory, antimagic labeling refers to assigning distinct positive integers to each newlinevertex and its edges in order to have a unique sum of labels incident to each vertex. newlineThis characteristic facilitates the analysis and differentiation of graphs.The study of antimagic newlinelabeling is primarily driven by its applications in network design, cryptography, newlineand resource allocation, where distinct identifiers or configurations serve a vital function newlinein upholding security and optimising performance. One of the main advantages of newlineantimagic labeling is that it uses edge labels to encode information, which helps with newlinegraph representation, data encoding, and combinatorial problems. The study on antimagic newlinelabeling naturally paves way for distance antimagic labeling which takes into newlineaccount the spatial interactions between vertices. This development demonstrates the newlinetheoretical depth and practical utility of antimagic labeling concepts. newlineThe initial component of the thesis examines the presence and absence of distance antimagic newlinelabeling in particular categories of graphs. This study uses computer tools to newlinefind distance antimagic labeling for two types of graphs: the Kneser graph and the bipartite newlineKneser graph. It also investigates distance antimagic labeling in certain classes newlineof graphs that are disconnected and gives results of labeling in graphs related to cycles. newlineIn the next section, distance antimagic labeling on various basic graph products is discussed. newlineThe graph products taken into consideration are the Cartesian product, tensor newlineproduct, lexicographic product, and strong product. Graph products are utilized in many newlineother fields and are crucial to graph theory. Graph products are used in network design... newline