Maximum Detour Index of Unicyclic Graphs with Given Maximum Degree

Abstract

The detour index of a connected graph is defined as the sum of detour distances between all its unordered vertex pairs. We determine the maximum detour index of \(n\)-vertex unicyclic graphs with maximum degree \(\Delta\), and characterize the unique extremal graph, where \(2 \leq \Delta \leq {n-1}\).