MIS, MVC and MDS in Cyclic Layered Graphs

Graphs are discrete objects with myriad applications in science and engineering. Several graph theoretic problems are shown to be hard. However, for restricted versions of graphs based on the type of restriction the problems that are hard to solve for a general graph become tractable. Layered graphs have been defined and are shown to have applications in social networks and computational molecular biology. We define a new class of graphs called cyclic layered graphs that are related to layered graphs. We pose three problems that can be modeled as graph theoretic problems on cyclic layered graphs. We design efficient algorithms for these problems.