The maximum Mostar indices of unicyclic graphs with given diameter

•The greatest Mostar index among the graphs with order n and diameter d is determined.•The graphs with the greatest Mostar index among the graph set above are determined.•Cut method and graph transformations are used. For an edge e=uv in a given graph G, let nGu(e) be the number of vertices which have a less distance from u than that from v. Then |nGu(e)−nGv(e)| is called the contribution of e. The Mostar index is defined as the sum of the edge contributions in G. In this paper, the unicyclic graphs with order n and diameter d, having the greatest Mostar index are determined.