Graphs of order n and diameter 2(n−1)/32(n−1)/3 minimizing the spectral radius

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. A minimizer graph is such that minimizes the spectral radius among all connected graphs on n vertices with diameter d  . The minimizer graphs are known for d∈{1,2}∪[n/2,2n/3−1]∪{n−k|k=1,2,…,8}d∈{1,2}∪[n/2,2n/3−1]∪{n−k|k=1,2,…,8}. In this paper, we determine all minimizer graphs for d=2(n−1)/3d=2(n−1)/3.