# The Schultz and the Modified Schultz Indices of Kragujevac Trees

Document Type : Research Paper

Author

اراک- خیابان قیام- خیابان شهروند-خیام 2پلاک 513

Abstract

Let G be simple connected graph with the vertex and edge sets V (G) and E(G), respectively. The Schultz and Modifi ed Schultz indices of a connected graph G are defi ned as Sc(G) =1/2 \sum_{u,v \in V} (d_u + d_v)d(u,v) and Sc*(G) = 1\2\sum_{u,v \in V}(d_u.d_v)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 Modifi ed Schultz indices of the Kragujevac trees is proposed. As application, we obtain an upper bound and a lower bound for the Schultz and the modi fied Schultz indices of this tree.

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