Broadcasting in computer networking means the dissemination of information, which is known initially only at some nodes, to all network members. The goal is to inform every node in the minimal time possible. There are few models for broadcasting; the simplest and the historical model is called the Classical model. In the Classical model, dissemination happens in synchronous rounds, wherein a node may only inform one of its neighbors. The broadcast question is: What is the minimum number of rounds needed for broadcasting, and what broadcast scheme achieves it?
For general graphs, these questions are NP-hard, and it is known to be at least 3 - ε inapproximable for any real ε > 0. Even for some very restricted classes of graphs, the questions remain as an NP-hard problem. Little is known about broadcasting in restricted graphs, and only a few classes have a polynomial solution.
Parallel and distributed computing is one of the important domains which relies on efficient broadcasting. Hypercube and torus are the most used network topology in this domain. The widespread use is not only due to their simplicity but also is for their efficiency and high robustness (e.g., fault tolerance) while having an acceptable number of links. In this thesis, it is observed that the Cartesian product of a number of path and cycle graphs produces a valuable set of topologies, we called hyper-cylinders, which contain hypercube and Torus as well. Any hyper-cylinder shares many of the beneficial features of hypercube and torus and might be a suitable substitution in some cases. Some hyper-cylinders are also similar to other practically used topologies such as cube-connected cycles. In this thesis, the effect of the Cartesian product on broadcasting and broadcasting of hyper-cylinders under the Classical and Messy models is studied. This will add a valuable class of graphs to the limited classes of graphs which have a polynomially computable broadcast time. In the end, the relation between worst-case originators and diameters in trees is studied, which may help in the broadcast study of a larger class of graphs where any tree is allowed instead of a path in the Cartesian product
