Observations in continuous monotonic decomposition of connected graphs special cases in complete tripartite graphs and other related topics

Abstract

Kasimir Kuratowski solved the characterization of the planar graphs in 1930. Hungarian Mathematician, Denes Konig published the first book on Graph Theory in 1936. Ever since this, there have been a lot of researches happened in the field of Graph Theory. As a result, it is one of the most fascinating branches of modern Mathematics. True its origin, it has wide variety of applications. Through the techniques of Graph Theory, a whole lot of problems in Electrical Networks, Coding Theory, Operations Research, Computer Programming, Computer Science, Chemistry, Social Sciences, Game Theory, Combinatorics, Mathematical and Non-Mathematical Puzzles etc. Many applications in Graph Theory involve large graphs that require the computationally intensive talents of a computer in conjunction with the ingenuity of mathematical methods. One of the major reasons for the enormous growth of interest in Graph Theory in the last couple of decades is the development of high-speed digital computers. It would have been much time consuming to find out several results in this thesis and to verify several others without the help of computer programming. newline