Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource PHD PhD PhD Thesis Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Relation A related resource No Thesis Title A name given to the resource Antimagic labeling and its variations in graphs Subject The topic of the resource Mathematics and Statistics Description An account of the resource Graph theory is a branch of discrete Mathematics with its results having significant applications in many areas of computing, social, and natural sciences. Graph labeling is one of the fascinating areas of graph theory with wide-ranging applications. The concept was first introduced in the 1960s where the vertices and edges are assigned real values or newlinesubsets of a set subject to certain conditions. The labeling dealt in the thesis is edge labeling basically, that is, assigning a label to the edges of the graph. Depending on the conditions applied in labeling give way to magic, super-magic, antimagic labelings. Hartsfield and Ringel introduced the notion of antimagic labeling in the year 1990. In this thesis, three variations in graph labeling are dealt namely, equitable antimagic labeling, equitable difference labeling and extension of equitable irregular labeling with an introduction of k-equitable irregular labeling. For a given graph G = (V,E), an equitable antimagic labeling (EAL) of G is a bijective edge-labeling f: E(G) and#8594; {1,2,3,...,m = |E(G)|} such that |W_f (u)-W_f (v)| and#8804; 1 for any pair of adjacent vertices u and v of G, where W_f (v) is the sum of the labels of the edges incident with the vertex v. A graph admitting an EAL is called an equitable antimagic graph (EAG). In Chapter 2, we initiate a study of this new edge labeling of graphs. A diand#64256;erence labeling of a graph G is realized by assigning distinct integer values to each vertex and then associating with each edge, the absolute diand#64256;erence of those values assigned to its end vertices. That is, it is an injective function f: V(G) and#8594; N together with function f^*: E(G) and#8594; N deand#64257;ned by f^* (uv)=|f(u)-f(v)|for any edge uv in G. The function f^* is called the weight function induced by f. An irregular labeling f: E(G) and#8594; N with the property that S_f (u) and#8800; S_f (v) for any two vertices u and v of G, where S_f (u) denotes the sum of the labels of the edges incident with the vertex u. The sum S_f (u) is called the vertex sum of u under f. Creator An entity primarily responsible for making the resource Puthussery, Antony. Source A related resource from which the described resource is derived Author's Submission Publisher An entity responsible for making the resource available Christ(Deemed to be University) Date A point or period of time associated with an event in the lifecycle of the resource 2019-01-01 Contributor An entity responsible for making contributions to the resource Hamid, I Sahul. Rights Information about rights held in and over the resource Open Access Format The file format, physical medium, or dimensions of the resource PDF Language A language of the resource English Type The nature or genre of the resource PhD Identifier An unambiguous reference to the resource within a given context <a href="http://hdl.handle.net/10603/426794" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/426794</a>