Sharp bounds on the zeroth-order general Randić indices of conjugated bicyclic graphs

The zeroth-order general Randić index of a (molecular) graph G is defined as ∑ v ∈ V ( G ) ( d ( v ) ) α , where d ( v ) is the degree of vertex v in G , and α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index of conjugated bicyclic graphs (i.e., bicyclic graphs with perfect matchings). We characterized the conjugated bicyclic graphs with maximum and minimum R α 0 according to α in different intervals.