doiSerbia

Reciprocal product-degree distance of graphs

Su Guifu (School of Mathematics, Beijing Institute of Technology, Beijing, P.R. China)
Xiong Liming (School of Mathematics, Beijing Institute of Technology, Beijing, P.R. China)
Gutman Ivan (Faculty of Science, Kragujevac)
Xu Lan (Changji University, Department of Mathematics, Xinjiang, P.R. China)

We investigate a new graph invariant named reciprocal product-degree distance, defined as: RDD* = Σ{u,v}V(G)u≠v deg(u)∙deg(v)/dist(u,v) where deg(v) is the degree of the vertex v, and dist(u,v) is the distance between the vertices u and v in the underlying graph. RDD* is a product-degree modification of the Harary index. We determine the connected graph of given order with maximum RDD*-value, and establish lower and upper bounds for RDD*. Also a Nordhaus-Gaddum-type relation for RDD* is obtained.

Keywords: distance (in graph), degree distance, product-degree distance, reciprocal degree distance, reciprocal product-degree distance