RECIPROCAL GUTMAN INDEX OF PRODUCTS OF COMPLETE GRAPHS

The Reciprocal Gutman Index (RGut), defined for a connected graph as vertex degree weighted sum of the reciprocal distances, i.e, ???? ( ? ) = ? ? ? ( ? ) ? ? ( ? ) ? ? ( ? , ? ) ? , ? ∈ ? ( ? ) . The RGut is a weighted version of the Harary index, just as the Gutman index is a weighted version of the Wiener index. In this paper, we present exact expression for the reciprocal Gutman index of Cartesian product and the wreath product of complete graphs with odd vertices interms of other g raphs invariants including the reciprocal degree distance, Harary index, the first Zagreb index and the second Zagreb index.