The regularity and unimodality of h-polynomial of corona graphs

Abstract

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.