  In this paper, we consider generalized domination structure in graphs, which
stipulates the structure of a minimum dominating set. Two cycles of length 0
mod 3 intersecting with one path are the constituents of the domination
structure and by taking every three vertices on the cycles we can obtain a
minimum dominating set. For a cubic graph, we construct generalized domination
structure by adding edges in a certain way. We prove that the minimum
dominating set of a cubic graph is determined in polynomial time.
