Abstract :

The set of all vertices in the graph G in which every two vertices are not adjacent is called independent set of vertices, and the maximum number of independent vertices by B0(G), similarly the set of all edges
in the graph G in which every two edges are not incident is called independent set of edges, and the maximum number of independent edges denoted by B1(G).
In this article we will investigate and determine the independent numbers of vertices and edges of certain types of graphs by classic graph definitions and by using characteristic polynomial of graphs.