Centers of Tensor Products of Graphs

Abstract

Formulas for vertex eccentricity and radius for the tensor product \(G \otimes H\) of two arbitrary graphs are derived. The center of \(G \otimes H\) is characterized as the union of three vertex sets of form \(A \times B\). This completes the work of Suh-Ryung Kim, who solved the case where one of the factors is bipartite. Kim’s result becomes a corollary of ours.