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On inverse degree and topological indices of graphs

Das Kinkar Ch. (Sungkyunkwan University, Department of Mathematics, Suwon, Republic of Korea)
Xu Kexiang (Sungkyunkwan University, Department of Mathematics, Suwon, Republic of Korea + College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu, PR China)
Wang Jinlan (Nanjing University of Aeronautics & Astronautics, College of Science, Nanjing, Jiangsu, PR China)

Let G=(V,E) be a simple graph of order n and size m with maximum degree Δ and minimum degree δ. The inverse degree of a graph G with no isolated vertices is defined as ID(G) = Σn,i=1 1/di, where di is the degree of the vertex viV(G). In this paper, we obtain several lower and upper bounds on ID(G) of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse degree ID(G) with topological indices (GA1-index, ABC-index, Kf-index) of graphs.

Keywords: Simple graph, Inverse degree, GA1-index, ABC-index, Kf-index, Vertex degree