الملخص

Restricted detour distance between two vertices    and of a graph  is the length of a longest u- v path  for the induced condition (V (P))=P. The restricted detour polynomial depends on restricted detour distance and is denoted by D*(G,x) and defined by D*(G,x) = ∑{u,v}xD*(u,v) where the summation is taken over all unordered pairs (u,v) of distinct vertices of u and v of V(G). In this paper, we investigate the restricted detour polynomial of the straight chain of wheel graphs φ(WkB) and compute the restricted detour index of φ(WkB).