Bicyclic graphs with extremal detour index - Du, Chunjuan (Utilitas Mathematica, 2014)
The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. We determine the graphs with the second and the third smallest and largest detour indices in the class of n-vertex bicyclic graphs with exactly two cycles for n ≥ 6.