Independence polynomials of graphs with given cover number or dominate number

For a graph Formula: see text, let Formula: see text be the number of independent sets of size Formula: see text in Formula: see text. The independence polynomial Formula: see text has been the focus of considerable research. In this paper, using the coefficients of independence polynomials, we order graphs with some given parameters. We first determine the extremal graph whose all coefficients of Formula: see text are the largest (respectively, smallest) among all connected graphs (respectively, bipartite graphs) with given vertex cover number. Then we also derive the extremal graph whose all coefficients of Formula: see text are the largest among all connected graphs (respectively, bipartite graphs) with given vertex dominate number.