Steiner Degree Distance of Two Graph Products

Abstract

Abstract The degree distance DD(G) of a connected graph G was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of k-center Steiner degree distance defined as SDD k ( G ) = ∑ S ⊆ V ( G ) | S | = k [ ∑ v ∈ S deg ⁡ G ( v ) ] d G ( S ) , SDD_k (G) = \sum\limits_{\mathop {S \subseteq V(G)}\limits_{\left| S \right| = k} } {\left[ {\sum\limits_{v \in S} {{\it deg} _G (v)} } \right]d_G (S),} where dG (S) is the Steiner k-distance of S and degG (v) is the degree of the vertex v in G. In this paper, we investigate the Steiner degree distance of complete and Cartesian product graphs.