On Inverse Degree and Topological Indices of Graphs

Kinkar Ch. Das, Kexiang Xu, Jinlan Wang

Let $G=(V,E)$ be a simple graph of order $n$ and size $m$ with maximum degree $\Delta$ and minimum degree $\delta$. The inverse degree of a graph $G$ with no isolated vertices is defined as \[ ID(G)=um_{n}^{i=1}\frac1{d_i}, \] where $d_i$ is the degree of the vertex $v_i\in V(G)$. 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 ($GA_1$-index, $ABC$-index, $Kf$-index) of graphs.