Kernel Set Problem and its Computation

Given with a graph G and its any isomorphic graph G', a minimum determiner set of G is a minimum set of vertices such that, if these vertices are assigned in one-to-one correspondence between G and G' then correspondences of the remaining vertices of G are uniquely determined. A kernel set is a minimum determiner set with the least number of elements. In this paper, we firstly define determiner set and minimum determiner set properly as well as kernel set. Then we show the related properties and propose algorithms to find minimum determiner set as a previous step toward finding kernel set. Finally, we give an example by applying proposed algorithms to show the usefulness of minimum determiner set as well as kernel set.