Extremal Hosoya index and Merrifield–Simmons index of hexagonal spiders

For any graph GG, let m(G)m(G) and i(G)i(G) be the numbers of matchings (i.e., the Hosoya index) and the number of independent sets (i.e., the Merrifield–Simmons index) of GG, respectively. In this paper, we show that the linear hexagonal spider and zig-zag hexagonal spider attain the extremal values of Hosoya index and Merrifield–Simmons index, respectively.