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The graph strong 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.
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