Computation of Detour D-Index and Average Detour D-Distance of Specific Graphs

The length of the longest u-v path in a connected graph Λ is the detour distance D(u,v) for any two different vertices u and v. The detour D-distance denoted by D^D (u,v) and defined by DD (u,v)=max⁡lD (P), where the maximum is taken over all uv paths P in Λ. The detour D-index of Λ is defined by W_D^D (Λ)=1/2 ∑_(u,v∈V(Λ))▒〖D^D (u,v)〗=∑_({u,v}⊆V(Λ))▒〖D^D (u,v)〗 . The detour D-index of several graphs, including the French windmill, Kulli-wheel windmill, lollipop, general barbell, and general modified barbell graphs is studied and obtained in this paper. Furthermore, these graphs average detour D-distance will be determined.