For a simple graph G, let \(J_G\) denote the corresponding binomial edge ideal. This article considers the binomial edge ideal of the corona product of two connected graphs G and H. The corona product of G and H, denoted by \(G\circ H\) , is a construction where each vertex of G is connected (via the coning-off) to an entire copy of H. This is a direct generalization of a cone construction. Previous studies have shown that for \(J_{G \circ H}\) to be Cohen–Macaulay, both G and H must be complete graphs. However, there are no general formulae for the dimension, depth, or Castelnuovo–Mumford regularity of \(J_{G\circ H}\) for all graphs G and H. In this article, we provide a general formula for the dimension, depth and Castelnuovo–Mumford regularity of the binomial edge ideals of certain corona and corona-type (somewhat a generalization of corona) products of special interests. Additionally, we study the Cohen–Macaulayness, unmixedness and related properties of binomial edge ideals corresponding to above class of graphs. We have also added a short note on the reduction of the Bolognini–Macchia–Strazzanti conjecture to all graphs with a diameter of 3.
