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We are living in a world where communication has become easy. All communication devices are connected to each other in ways which were earlier considered impossible. Graph theory is at the core of this vast connectivity. It breaks down the complex connections into simpler modules which can be understood easily. Hamiltonian graphs, which is the subject of discussion in this book, is a part of graph theory. Hamiltonian graphs are special graphs where we start from the starting vertex and after traversal of all other vertices we reach the starting vertex at the end. There are several applications such as mobile networks, time-table matching,line graphs, complete regular Hamiltonian graphs etc which are discussed in this text book.