atom-bond connectivity spectral radius

The ABC (atom-bond connectivity) spectral radius ρ_ABC of a graph is defined as the largest eigenvalue of its ABC matrix. Chen showed that for a tree on 3 or more vertices, sqrt(2)cos(π/(n + 1))<=ρ_ABC(T)<=sqrt(n - 2), where the lower bound corresponds to the ABC spectral radius of the path graph P_n and the upper to that of the star graph S_n .

ABC matrix | graph eigenvalue | spectral radius