A graph is reducible if it can be reduced to only one vertex by means of a sequence of transformations and series-parallel reductions. It is known that every plane graph satisfies this property. In this paper, we generalize the definition of transformation in a graph to that of n-polygon �n-star transformation, and explore the case We study some families of graphs which are 4-polygon reducible, in particular, cubic and quasi-cubic gramineous graphs. We also exhibit the families of quasi-cubic graphs which are not 4-polygon reducible, and non-4-polygon reducible cubic graphs which are minimal with respect to the number of vertices.
