Let H = {Hv : v ∈ V (G)} be a family of nonempty graphs indexed by the vertex set of a graph G. The corona graph G ◦ H of G and H is the disjoint union of G and Hv, v ∈ V (G), with additional edges joining each vertex v ∈ V (G) to all the vertices of Hv. In this paper, we are deeply concerned in investigating the (induced) matching number of the graph G ◦ H. It gives a formula for the Castelnuovo–Mumford regularity of edge ideal of this graph. Additionally, we propose a close relationship between independence polynomial of corona graph G ◦ H and h-polynomial of its independence simplicial complexes. Thereby, the formula of h-polynomial of G◦H is established and some properties of its unimodality and real-rootedness are presented.