The Schultz and the Modified Schultz Indices of Kragujevac Trees

Let 𝐺 be simple connected graph with the vertex and edge sets 𝑉(𝐺) and 𝐸(𝐺), respectively. The Schultz and Modified Schultz indices of a connected graph 𝐺 are defined as 𝑆𝑐(𝐺) =1/2 ∑𝑢, 𝑣∈𝑉 (𝐺) (𝑑𝑢 + 𝑑𝑣) 𝑑 (𝑢,𝑣) and 𝑆𝑐*(𝐺) = 12∑𝑢,𝑣∈ 𝑉 (𝑑𝑢×𝑑𝑣) 𝑑 (𝑢, 𝑣), where 𝑑(𝑢, 𝑣) is the topological distance between vertices 𝑢 and 𝑣, d_𝑣 is the degree of vertex 𝑣 of 𝐺. In this paper, computation of the Schultz and Modified Schultz indices of the Kragujevac trees is proposed. As application, we obtain an upper bound and a lower bound for the Schultz and the modified Schultz indices of this tree.