Bicyclic Graphs With Minimal Values of the Detour Index

Žana Kovijanić Vukićević, Vladimir Božović

We are looking for the graphs with minimal detour index in the class of connected bicyclic graphs. For the fixed number of vertices, we split the problem into two cases: bicyclic graphs without common edges between cycles and the complement of it. In both cases, we find graphs with minimal detour index.