A Study of Mathematical Graph Theory Labeling: Exploring Various Graph Labeling Problems

Abstract

A graph labeling is an assignment of integers to the vertices or edges or both, subject to certain conditions have been motivated by practical problems, labeled graphs serve useful mathematical models for a broad range of applications such as coding theory, including the design of good types codes, synch-set codes, missile guidance codes and convolutional codes with optimal auto correlation properties. Graph theory has applications in many areas of the computing, social and natural science. The theory is also intimately related to many branches of mathematics, including matrix theory, numerical analysis, probability, topology and combinatory. The fact is that graph theory serves as a mathematical for any system involving a binary relation. Over the last 50 year graph theory has evolved into an important mathematical tool in the solution of a wide variety of problems. Difference labelings of a graph C are acknowledged by appointing unmistakable whole number qualities to every vertex and afterward connecting with each edge the supreme distinction of those qualities doled out to its end vertices. Right now explore the presence of labelings for cycles, cartesian result of two graphs, rn-crystals, rectangular matrices and n-solid shapes which deteriorate these graphs into indicated parts. We likewise examine the comparing issue for added substance labelings.