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

Graph theory plays a significant role in variety of real-world systems. concepts such as labeling and coloring are used to depict processes relationships material, social, biological, physical, information Specifically, graph is communication network addressing, fault-tolerant system design, automatic channel allocation, etc. 2-odd assigns distinct integers the nodes manner, that positive difference adjacent either 2 or an odd integer, src=image/13427595_02.png>, src=image/13427595_03.png>. So, src=image/13427595_04.png> if only it permits labeling. Studying certain important modifications through various operations on given interesting challenging. These mainly modify underlying graph's structure, so understanding complex can be done over set graphs inevitable. The motivation behind development this article apply concept generated by using operations. Further, results also derived some well-known number theoretic Twin prime conjecture Goldbach's conjecture, besides recalling few applications coloring.