In order to solve some problems, as well as to simplify or facilitate some analyses in graphs, some changes can be made in the graphs. Dual graph is one of these changes. Linear dual graph is a type of dual graph that is proposed for presenting graphs with weighted nodes. In this paper, linear dual graph calculus that is based on the linear dual graph is introduced. For this purpose, at first, Linear Dual (LD1) and inverse Linear Dual (LD-1) is introduced, and then, the way of their extraction is explained. After that some applications of this calculus is explained. One of its most important applications is in specification the Hamiltonian cycle in graphs. In other words, by transportation between linear dual graph and the primal graph,we can convert the Hamiltonian cycles whose specification has always been so difficult, to Eulerian ones which can be easily recognized.
)