Application of Graph Theory to facebook with Special reference to the application of Mengers and Ores Theorem

Abstract

Our Thesis links two apparently distinct branches Face book and Mathematics. The work newlinepresented here is about application of mathematics to face book network, not every branch of newlinemathematics finds its application to face book network. A branch of mathematics called newline Graph Theory can be naturally applied to face book network, our thesis is in this direction. The newlinepresent work is carried out by translating a face book network to a corresponding graph and newlineconversely. In this process we have shown that some complicated face book network can be newlineeasily understood and interpreted in terms of a corresponding graph. Also we have shown how newlinesome interesting graphs can be interpreted in terms of face book networks, focusing specially on newlinethe application of graph to coding. We have also demonstrated how face book network and graph newlinetheory are mutually benefitted by the 2-way translations. We have shown that some difficult newlinetheorems in graph theory like Ore s theorem, Menger s theorem and Hand Shaking Theorem newlinebecome simple and natural when they are translated to face book network, equivalently the newlinediscussion among the face book users at a given time can be easily understood by others by newlinetranslation of face book network to graph. In the process of mutual translations we have newlineinterpreted L-Matrix and a proposition on it to face book network and demonstrated how a new newlineresult is obtained. We have also demonstrated how magic squares lead to different kinds of newlinedecorations by translating the magic square into corresponding graphs. Conversely any graph newlinetheorist can easily obtain a magic square looking at a decoration in any function. In fact the newlineprocess of translation can help in communicating various events in a function/meeting/an newlineinterview to outsiders. newline