Thanks for the answer Chip! Of course I created my own function for calculate the Strong Product, even if my code is a bit different from yours. But they are equivalent I guess. I was just surprised that exist a sort of reference about a build-in function that does not exist really. Thank you again! Anyway that is my function to get the Strong Product

GraphStrongProduct[G_, H_] :=

 Module[{ajmG, ajmH, ajm1G, ajm1H, P, ajmGH} ,
         (* give the adjacency matrix of the graphs*)

  ajmG = Normal[ArrayFlatten[AdjacencyMatrix[G]]];
              ajmH = Normal[ArrayFlatten[AdjacencyMatrix[H ]]];
         (* give the modified adjacency matrix of the graphs, 
  1 on the diagonal*)
         ajm1G = ReplacePart[ajmG, {i_, i_} -> 1];
         ajm1H = ReplacePart[ajmH, {i_, i_} -> 1];
         (*the adjacent matrix of the strong product between G and H*)
    \
       P = ArrayFlatten[TensorProduct[ajm1G, ajm1H]];
         ajmGH = ReplacePart[P, {i_, i_} -> 0];
         AdjacencyGraph[ajmGH]
  ]

It seems work too.

You can get around 1.5 times faster if you avoid the pattern matcher by replacing the lines containing ReplacePart with the following:

Change

ajm1G = ReplacePart[ajmG, {i_, i_} -> 1];
ajm1H = ReplacePart[ajmH, {i_, i_} -> 1];

to

ajm1G = Unitize[ajmG + IdentityMatrix[Length[ajmG]]];
ajm1H = Unitize[ajmH + IdentityMatrix[Length[ajmH]]];

and

ajmGH = ReplacePart[P, {i_, i_} -> 0];

to

ajmGH = P (1 - IdentityMatrix[Length[P]]);