On the inverse degree index and decompositions in graphs.

The inverse degree index of a graph G=(V,E) without isolated vertices is defined as ID(G)=ΣvЄv1/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. [ABSTRACT FROM AUTHOR]