Ordering of Hosoya indices for unicyclic Hückel graphs

The unicyclic graphs with perfect matchings having degrees not greater than three are referred to as the unicyclic Hückel graphs. The set of these graphs with 2n2n vertices is denoted by H2nH2n. By a new method proposed here, we obtain the first 7 graphs in the increasing order of their Hosoya indices within H2nH2n for n≥8n≥8. In addition, complete increasing orders of graphs in terms of their Hosoya indices are also derived for four subsets in H2nH2n.