Antimagic labeling and its variations in graphs

Title

Antimagic labeling and its variations in graphs

Creator

Puthussery, Antony.

Contributor

Hamid, I Sahul.

Description

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.

Source

Author's Submission

Date

2019-01-01

Publisher

Christ(Deemed to be University)

Subject

Mathematics and Statistics

Rights

Open Access

Relation

No Thesis

Format

PDF

Language

English

Type

PhD

Identifier

http://hdl.handle.net/10603/426794