### Journals Information

**
Mathematics and Statistics Vol. 10(4), pp. 875 - 883 DOI: 10.13189/ms.2022.100419 Reprint (PDF) (480Kb) **

## 2-Odd Labeling of Graphs Using Certain Number Theoretic Concepts and Graph Operations

**Ajaz Ahmad Pir ^{1}, Tabasum Mushtaq ^{2}, A. Parthiban ^{1}^{,*}**

^{1}Department of Mathematics, Lovely Professional University, Phagwara 144 411, Punjab, India

^{2}Department of Statistics, Govt. Degree College, Sopore 193 201, Jammu and Kashmir, India

**ABSTRACT**

Graph theory plays a significant role in a variety of real-world systems. Graph concepts such as labeling and coloring are used to depict a variety of processes and relationships in material, social, biological, physical, and information systems. Specifically, graph labeling is used in communication network addressing, fault-tolerant system design, automatic channel allocation, etc. 2-odd labeling assigns distinct integers to the nodes of in such a manner, that the positive difference of adjacent nodes is either 2 or an odd integer, , . So, is a 2-odd graph if and only if it permits 2-odd labeling. Studying certain important modifications through various graph operations on a given graph is interesting and challenging. These operations mainly modify the underlying graph's structure, so understanding the complex operations that can be done over a graph or a set of graphs is inevitable. The motivation behind the development of this article is to apply the concept of 2-odd labeling on graphs generated by using various graph operations. Further, certain results on 2-odd labeling are also derived using some well-known number theoretic concepts such as the Twin prime conjecture and Goldbach's conjecture, besides recalling a few interesting applications of graph labeling and graph coloring.

**KEYWORDS**

2-odd Labeling, Mobius Ladder, Union, Intersection, Duplication, Extension, Twin Prime Conjecture, Goldbach's Conjecture

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Ajaz Ahmad Pir , Tabasum Mushtaq , A. Parthiban , "2-Odd Labeling of Graphs Using Certain Number Theoretic Concepts and Graph Operations," Mathematics and Statistics, Vol. 10, No. 4, pp. 875 - 883, 2022. DOI: 10.13189/ms.2022.100419.

(b). APA Format:

Ajaz Ahmad Pir , Tabasum Mushtaq , A. Parthiban (2022). 2-Odd Labeling of Graphs Using Certain Number Theoretic Concepts and Graph Operations. Mathematics and Statistics, 10(4), 875 - 883. DOI: 10.13189/ms.2022.100419.