A note on ABC spectral radii of unicyclic graphs

The ABC spectral radius of a graph G is the largest eigenvalue of the
ABC matrix modified from the adjacency matrix of G so that the
(u,v)-entry is
√(d_{u}+d_{v}-2)/√d_{u}d_{v}
for an edge uv, where d_{w} is the degree of vertex w in G.
We show that the graph formed from a cycle of length n-p by attaching p
pendent edges to a vertex uniquely maximizes the ABC spectral radius
over all n-vertex unicyclic graphs with p pendant edges, and over all
n-vertex unicyclic graphs with girth n-p, respectively.