Schultz polynomials and their topological indices of bottleneck graphs

Let G = (V,E ) be a simple connected graph. The degree of a vertex u and the distance between the vertices u and v are denoted by du and d(u, v) of a graph G respectively. The Schultz and modified Schultz polynomials are and respectively. Then their first derivative at x = 1 are equals to and are known as Schultz index and modified Schultz index respectively. In this article, we compute the Schultz and modified Schultz polynomials and their indices for the bottleneck graphs K2◦Kn, ∀n∈N,K2◦Kn, n∀n∈N and K2◦Km, n∀m,n∈N, m ≠ n.