International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) | IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 5 | Iss.7| July 2015 | 1| Applications of Bipartite Graph in diverse fields including cloud computing 1 Arunkumar B R, 2 Komala R Prof. and Head, Dept. of MCA, BMSIT, Bengaluru-560064 and Ph.D. Research supervisor, VTU RRC, Belagavi Asst. Professor, Dept. of MCA, Sir MVIT, Bengaluru and Ph.D. Research Scholar,VTU RRC, Belagavi I. INTRODUCTION Graph theory has emerged as most approachable for all most problems in any field. In recent years, graph theory has emerged as one of the most sociable and fruitful methods for analyzing chemical reaction networks (CRNs). Graph theory can deal with models for which other techniques fail, for example, models where there is incomplete information about the parameters or that are of high dimension. Models with such issues are common in CRN theory [16]. Graph theory can find its applications in all most all disciplines of science, engineering, technology and including medical fields. Both in the view point of theory and practical bipartite graphs are perhaps the most basic of entities in graph theory. Until now, several graph theory structures including Bipartite graph have been considered only as a special class in some wider context in the discipline such as chemistry and computer science [1]. This effort deals exclusively with bipartite graphs and its applications in cloud computing. It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. It is showed in paper [17] that any complex network can be modeled using bipartite graph with some specifications. It also implies that you have always have got alternate graph theory structure to replace some structure which is not suitable that is also from graph theory. The next subsection brings the bipartite graph with its definition, uniqueness and characteristics. 1.1 Bipartite Graph In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets U and V (that is, U and V are each independent sets such that every edge connects a vertex in U to one in V. Vertex set U and V are often denoted as partite sets. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles [1], [2]. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V green, each edge has endpoints of differing colors, as is required in the graph coloring problem.[3][4] In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle after one node is colored blue and another green, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E)to denote a bipartite graph whose partition has the parts U and V, with Edenoting the edges of the graph. If a bipartite graph is not connected, it may have more than one bipartition; in this case, the (U,V,E) notation is helpful in specifying one particular bipartition that may be of importance in an application. If │U│=│V│, that is, if the two subsets have equal cardinality, then Gis called a balanced bipartite graph.[3]. If all vertices on the same side of the bipartition have the same degree, then Gis called bi-regular. The given item to be searched in cloud can be modeled as a bipartite cloud, further, perfect matching algorithms, theorems and lemmas can obviously mathematically modeled and analyzed. A bipartite graph G = (U; V;E) is specified by two disjoint sets U and V of vertices, and a set E of edges between them. A perfect matching is a subset of the edge set E such that every vertex has exactly one edge incident on it. Since we are interested in perfect matching’s in the graph G, we shall assume that |U| = |V |= n. Let U = {u1; u2; _ _ _ ; un} and V = {v1; v2; _ _ _ ; v n }. The algorithm has no error if G does not have a ABSTRACT: Graph theory finds its enormous applications in various diverse fields. Its applications are evolving as it is perfect natural model and able to solve the problems in a unique way.Several disciplines even though speak about graph theory that is only in wider context. This paper pinpoints the applications of Bipartite graph in diverse field with a more points stressed on cloud computing. KEY WORDS: Graph theory, Bipartite graph cloud computing, perfect matching applications