Reciprocal sterner degree distance

Abstract

The concept of Kcenter Steiner degree distance, introduced by Gutman, is a natural generalization of classical degree distance. In this paper, we introduce the concept of fc-center reciprocal Steiner degree distance of a graph. The k-center reciprocal Steiner degree distance RSDDk(G) of a connected graph G is defined by RSDDk(G) = £S£V(G) (£.,gS degG(v)) 5-7, |S|=fc where dc(S) is the Steiner fc-distance of S and degdy) is the degree of the vertex v ia G. Expressions for RSDDu for some special graphs are obtained. We also give shaip upper and lower bounds of RSDDk of a connected graph, and establish some of its properties in the case of trees. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.