A study on magic labeling of graphs using non abelian groups
| dc.contributor.advisor | Anil Kumar V | |
| dc.contributor.author | Anusha C | |
| dc.date.accessioned | 2026-02-03T10:03:18Z | |
| dc.date.issued | 2025 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12818/3120 | |
| dc.language.iso | en_US | |
| dc.publisher | Department of Mathematics, University of Calicut | |
| dc.title | A study on magic labeling of graphs using non abelian groups | |
| dc.type | Thesis | |
| dcterms.abstract | Graph labeling is an emerging area in graph theory research. Graph labeling is a mathe- matical technique that assigns labels to vertices, edges, or both, subject to specific conditions. One of the most interesting areas of graph labeling is the study of magic labeling. A finite connected simple graph G is said to be a magic graph if there exist real numbers, the edge labels of G with the following properties. (1) Different edges have different labels (2) The sum of the label values assigned to all edges, which are in incidence to the certain vertex, is the same for all vertices of graph G. Motivated by this definition, the area of group magic labeling of graphs has been developed. The magic labeling of graphs using abelian groups is a well-established research area in graph theory. This involves labeling the edges (or vertices) of a connected simple graph G with the non-identity elements of a finite abelian group A in such a way that the sum of the labels incident to each vertex (or edge) is constant for all vertices (or edges) of G. This thesis attempts to generalize the magic labeling of graphs using finite abelian groups to any finite group (abelian or non-abelian) A. Since the group operation of a non-abelian group is not commutative, investigating group magic labeling of graphs using a finite non- abelian group is an interesting research topic. When defining group magic labeling for graphs with finite groups, it is crucial to ensure consistency with the existing definition of A-magic labeling, where A is a finite abelian group, as established by S. M. Lee, Doob, and others. If the group A is non-abelian, then from the definition of A-magic labeling, it follows that the sum of the labels of edges or the sum of the labels of adjacent vertices incident to a particular vertex or edge may change according to the order in which we sum. To address this, we impose an additional ordering in the magic labeling. This thesis introduces the concept of A-magic labeling of graphs with a finite non-abelian group A. Specifically, the non-abelian groups S3 , D4 , and Q8 are considered, and necessary and sufficient conditions are determined for several well-known graphs to be S3 -magic, D4 - magic, and Q8 -magic. This thesis also discusses the idea of induced S3 -magic labeling of graphs and extends the concept of A-barycentric magic labeling of graphs with abelian groups to any finite group by defining the same for non-abelian groups. Furthermore, this study introduces a new magic labeling concept called conjugate A-magic labeling of graphs and investigates the conjugate S3 -magic labeling of some well-known graphs. Additionally, a study of neighborhood magic labeling of graphs using the finite non-abelian group A is also included in this thesis. |