IJFANS International Journal of Food and Nutritional Sciences

ISSN PRINT 2319 1775 Online 2320-7876

GRACEFUL LABELLING FOR CERTAIN GRAPHS

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SUDHA. S,Dr. AHIMA

Abstract

The study of famous K¨onigsberg bridge problem have been enunciated by L. Euler in 1736 and he has invented the technique to solve complicated problems. It directly pose a concern to such problem. After it no more efforts were made in the field of graph theory for about hundred years. In 1847 G. R. Kirchhoff enhanced the theory of trees for the applications in electrical circuit and networks. Ten years later, A. Cayley have found trees while he was trying to set out the isomers of hydrocarbons. The explosion of the computer age accelerated the growth of graph theory. Graph theory has a wide range of applications in computer science, electrical networks, and social sciences. Graphs have been shown to be an useful mathematical tool for explaining the structure of molecules in biology and chemistry. In one of his lectures in 1840, A. F. Mobius introduced the famous four-color dilemma. A. De Morgan addressed the issue with his colleagues mathematicians in London a decade later. De Morgan's explanation is credited as being the first systematic representation of the four-color issue. This issue has spurred graph theory research. The well-known four-color issue took a hundred years to solve. This issue was addressed in 1976 by W. Haken and K. Appel. They've created an artificial map in which four colours aren't enough to depict separate regions with different hues.

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