The Schultz and the Modified Schultz Indices of Kragujevac Trees

Document Type : Research Paper

Author

Arak Uinversity of Technology, Arak, Iran.

Abstract

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) = 1\2∑u,v∈ V(du×dv)d(u, v), where d(u, v) is the topological distance between vertices u and v, dv 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.

Keywords


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