On the inverse degree index and decompositions in graphs - Jesús Romero-Valencia; Juan C. Hernández-Gómez; Gerardo Reyna-Hernández (Kuwait Journal of Science)
The inverse degree index of a graph $G=(V,E)$ without isolated vertices is defined as $\ID(G)=\sum_{v\in V}\frac{1}{dv}$, where $dv$ is the degree of the vertex $v$ in $G$. In this paper, we show a relation between the inverse degree of a graph and the inverse degree indices of the primary subgraphs obtained by a general decomposition of $G$, we establish some relations between the inverse degree index and other known indices and an application to a specific chemical structure is given.