The isodominism class of the graphs.

In this paper, the new concept i -isodominism between two graphs is introduced, where i is a positive integer. The i -isodominism is a pair of the graph isomorphism which depends on the smallest i -dominating sets. By this tool, a graph with one vertex, complete graphs, wheels and stars are in the same 1 -isodominism class. Furthermore, some results about the 1 -isodominism classes of paths, cycles and star polygon are presented. [ABSTRACT FROM AUTHOR]