This paper has a double purpose. In the first part of the paper we give an overview of different aspects of graph theory which can be applied in communication engineering, not trying to present immediate results to be applied neither a complete survey of results, but to give a flavor of how graph theory can help research in optical networks. The second part of this paper is a detailed example of the usage of graph theory, but it is also a complete survey of recent results in minimization of the number of add--drop multiplexers (ADMs) required in a WDM ring with traffic grooming.