The graph strong product, also known as the graph AND product or graph normal product, is a graph product variously denoted ,
(Alon, and Lubetzky 2006), or (Beineke and Wilson 2004, p. 104) defined by the adjacency
relations (
and )
or (
and )
or (
and ).

In other words, the graph strong product of two graphs and has vertex set and two distinct vertices and are connected iff they are
adjacent or equal in each coordinate, i.e., for , either or , where is the edge set of .

Alon, N. and Lubetzky, E. "The Shannon Capacity of a Graph and the Independence Numbers of Its Powers." IEEE Trans. Inform.
Th.52, 2172-2176, 2006.Beineke, L. W. and Wilson, R. J.
(Eds.). Topics
in Algebraic Graph Theory. New York: Cambridge University Press, p. 104,
2004.Hammack, R.; Imrich, W.; and Klavžar, S. Handbook
of Product Graphs, 2nd ed. Boca Raton, FL: CRC Press, 2016.