Bicyclic graphs with small positive index of inertia

The positive index of inertia of a graph G, denoted by i+(G), is the number of the positive eigenvalues of the adjacency matrix of G. In this paper, we investigate the minimal positive index of inertia among all bicyclic graphs of order n with pendant vertices, and characterize the bicyclic graphs with positive index 1 or 2 among all bicyclic graphs of order n.