Study on hamiltonicity of regular graphs

Abstract

The study of graphs is a fundamental branch of Discrete Mathematics. newlineThe origin of graph theory was started with Konigsberg bridge newlineproblem.The Pregel River across the town of Konigsberg in Russia has newlinetwo islands connected by seven bridges. The problem was to begin at newlineany of the four land areas, walk across each bridge exactly once and newlinereturn to the starting point.The Swiss mathematician Leon-hard Euler newline(1707-1783) gave perceptions to this puzzle and the technique he approached newlineto resolve this is regarded as the birth of Graph theory. The newline_rst paper in graph theory titled \The solution of a problem relating newlineto the geometry of positionquot, deals with the famous Konigsberg bridge newlineproblem. newlineIn 1936, D_enes Konig, a German mathematician wrote the _rst book newlinein graph theory. Its English translation, \Theory of _nite and in_nite newlinegraphsquot was brought out later in 1990 by Richard Mc Coart [22]. Since newlinethen graph theory has become a nourishing, considerable and popular newlinebranch of Mathematics, Computer science and other areas. Many vol newlineumes have been written on the rich theory and many applications of newlinegraphs ( [81], [74], [33], [23]), including the pioneer works of C.Berge newline[13], F. Harary [32] and O.Ore [75]. newlineSylvester [74] used the term graph for therst time to represent newlinechemical formulae in the factors of graphic notation. The user interface newlineof graph theory in modeling real-world problems, along with the fast newlinegrowth of digital technology gained a unique position in the area of newlinemodern applied mathematics. With its numerous theoretical evolutions newlineand practical applications, the research on graph theory has undergone newlinea panoptic and global expansion in the last two centuries. newlineGraph theory is one of the subjects in Mathematics. In discrete newlinemathematics, the study of graphs has become an important topic. Generally,a graph constitutes a set of nodes joined by links. Therefore newlinegraphs are used in representing couplet correlation between the entities. newlineMany practical problems can be modeled using graph theory.