This paper gives an overview of the applications of graph theory in heterogeneous fields to some extent but mainly focuses on the computer science applications that uses graph theoretical concepts. In a Hamiltonian cycle, some edges of the graph can be skipped. In our researches, we have identified different types of graphs that are used in most important real field applications and then tried to give their clear idea from the Graph Theory. Note − Euler’s circuit contains each edge of the graph exactly once. Hamiltonian graph: A connected graph G= (V, E) is said to be Hamiltonian graph, if there exists a cycle which contains all vertices of graph G. Such a cycle is called Hamiltonian cycle. Properties of Hamiltonian graph. Sylvester in 1878 where he drew an analogy between Materials covering the application of graph theory “Quantic Invariants” and co-variants of algebra and often fail to describe the basics of the graphs and their molecular diagrams. It is a well known First, we define Hamilton fuzzy cycle as follows. This are entities such as Users, Pages, Places, Groups, Comments, Photos, Photo Albums, Stories, Videos, Notes, Events and so forth. Functions Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Keywords Hamiltonian, Regular, Edge-disjoint Hamiltonian circuits, Perfect matching, Intersection graph. Graphs are used to model many problem of the real word in the various fields. 1. Keywords : Bipartite Graph, Connected Graph, Social Media Networks, Graph Coloring, Median Graph. Example. A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. A connected graph is said to be Hamiltonian if it contains each vertex of G exactly once. applications of Graph Theory in the different types of fields. A node is whatever you are interested in: person, city, team, project, computer, etc. We discuss conditions for a fuzzy graph to have a particular type of Hamilton cycle called as Hamilton fuzzy cycle, based on the vertex neighbor sets of the fuzzy graph. 2 What is a Graph? But, maths is the universal language which is applied in almost every aspect of life. You read it right; basic mathematical concepts are followed all the time. Such a path is called a Hamiltonian path. Anyhow the term “Graph” was innovated by where those concepts are used in real life applications. Yes! The Graph API is a revolution in large-scale data provision. As in classical case, a fuzzy graph is said to be Hamiltonian if it contains a Hamilton cycle[27]. For example, the position of a planet is a function of time. According to some people, maths is just the use of complicated formulas and calculations which won’t be ever applied in real life. Hamiltonian fuzzy graphs. Hamiltonian Path − e-d-b-a-c. Facebook's Graph API is perhaps the best example of application of graphs to real life problems. INTRODUCTION Hamiltonian graph plays a very important role in real life’s problem. It is known that a Hamiltonian graph is a graph having at least one Hamiltonian circuit. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. Example. A graph is a collection of nodes and edges.A graph is also called a network. Graphs are extremely power full and yet flexible tool to model. On The Graph API, everything is a vertice or node. Applications. Real Life Applications of Trigonometry Graphs By: Kaleo Nakamura Cosine Graph Trigonometry y=cosx, cosx=sin(x+pi/2), y=Acos(Bx-C), y=Acos(Bx-C)+D A=Amplitude, B=Period/Number of Cycles, C=Phase Shift (Horizontal), D=Phase Shift (Vertical), C/B=Starting Point X=Value of X where An edge represents a relationship between nodes. 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