ABSTRACT
Studies of how particular graphical parameters interact with graph products have been the impetus for several areas of research in graph theory. Notable examples of this are the Shannon capacity of a graph, which is a certain limiting value involving the vertex independence number of strong product powers of a graph, and Hedetniemi’s coloring conjecture for the categorical product. One of the oldest unsolved problems in domination theory also comes from the area of graph products. Recently there has been renewed interest in a question first asked by V. G. Vizing [17] in 1963. Five years later he offered it as a conjecture [18], and in 1978 E. Cockayne included the conjecture as Problem 1 in his survey article [3].
