The Categorical Product of Graphs

Abstract

Undirected graphs and graph homomorphisms as introduced by Sabidussi ( 6 , p. 386), form a category that admits a categorical product. For the category of graphs and full graph homomorphisms, the categorical product was introduced by Čulik ( 1 ) under the name cardinal product . It was independently defined by Weichsel ( 8 ) who called it the Kronecker product and investigated the connectedness of products of finitely many factors. Hedetniemi ( 4 ) was the first to make use of the fact that the cardinal product is categorical.