Degree Distance of Tensor Product and Strong Product of Graphs

Abstract

In this paper, we determine the degree distance of $G\times K_{r_0,r_1,\ldots,r_{n-1}}$ and  $G\boxtimes K_{r_0,r_1,\ldots,r_{n-1}},$ where $\times$ and $\boxtimes$ denote the tensor product and strong product of graphs, respectively, and $K_{r_0,\,r_1,\,\ldots,\,r_{n-1}}$ denotes the complete multipartite graph with  partite sets $ V_0, V_1,\ldots,V_{n-1}$ where $|V_j|=r_j,~~ 0\leq j\leq n-1$ and $n\geq 3.$ Using the formulae obtained here, we have obtained the exact value of the degree distance of some classes of graphs.