The regularity and unimodality of h-polynomial of corona graphs

Let Formula: see text be a family of nonempty graphs indexed by the vertex set of a graph Formula: see text. The corona graph Formula: see text of Formula: see text and Formula: see text is the disjoint union of Formula: see text and Formula: see text, Formula: see text, with additional edges joining each vertex Formula: see text to all the vertices of Formula: see text. In this paper, we are deeply concerned in investigating the (induced) matching number of the graph Formula: see text. It consequently gives an explicit formula to compute the Castelnuovo–Mumford regularity of edge ideal of this graph. Moreover, we propose a close relationship between independence polynomial of corona graph and Formula: see text-polynomial of its independence simplicial complexes. Thereby, the formula of Formula: see text-polynomial is established and some results related to the unimodality and real-rootedness are presented.