New graph families satisfying the conditions of certain graph labeling techniques

Abstract

quotBackground: The development of graph theory is very similar to the development of newlineprobability theory, where much of the original work was motivated by efforts to understand newlinegames of chance. Essentially, graph theory is discovered by the Swiss mathematician Leon- newlinehard Euler during the course of finding a solution to the famous K¨onigsberg bridge problem newlinein 1736. In 1878, Sylvester was the first person who used the term graph in his paper. The newlinefirst textbook on graph theory was written by D´enes Kand#733;onig and was published in 1936. newlineAnother book was authored by Frank Harary was published in 1969, which is used widely newlinein the study of graph theory. newlineFurther, most graph labeling techniques trace their origin to labeling presented by AlexRosa[16] in 1967. In the mid 1960s graph labelings were first introduced. In the intervening newline50 years, over 200 graph labelings techniques have been studied in over 2500 papers. Graph newlinelabeling has vital applications in different fields such as like coding theory, X-ray crystal- newlinelography, communication network addressing, radar, astronomy, circuit design, database newlinemanagement etc. Moreover graph theory is also used in important major areas of computer newlinescience like data mining, image processing, optimal analysis, cryptography, software testing, newlineinformation security and communication networks. newlineAim: Prime aim of this research work is to analyze certain existing graph labeling tech- newlinenique and then to discover several new graph families which gratify the vital conditions for newlinespecific labeling. Further verification of the conditions of a certain graph labeling are pre- newlineserved under various operations on different graph families is one of the goal of this project. newlineMaterials and Methods: Initially reading of books and analysis of research papers pub- newlinelished in the reputed journals for the corresponding concepts were adopted to get proper newlinedirectional approach for the presented research work. Later case study, observation, ex- newlinetension and modification process were used for further research work.