Tomography on Finite Graphs

This paper focuses on tomography of functions on finite graphs. Graphs are discrete topological objects, which provide mathematical tools for the analysis of circuits and networks. The main problem in tomography on a graph deals with the reconstruction of a function defined on vertices of this graph and weights of edges from summations of these values along paths and cycles on this graph. We introduce some definitions of the problems, examples and open problems for tomography on finite graphs.