Extremal catacondensed benzenoids with respect to the Mostar index

Abstract

For a given graph G, the Mostar index $$Mo(G)$$ is the sum of absolute values of the differences between $$n_u(e)$$ and $$n_v(e)$$ over all edges $$e = uv$$ of G, where $$n_u(e)$$ and $$n_v(e)$$ are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. In this paper, the tree-type hexagonal systems (catacondensed hydrocarbons) with the least and the second least Mostar indices are determined. We also show some properties of tree-type hexagonal systems with the greatest Mostar index. And as a by-product, we determine the graph with the greatest Mostar index among tree-type hexagonal systems with exactly one full-hexagon. These results generalize some known results on extremal hexagonal chains.