In this paper we define a new dimension of graphs based on the strong product. Strong product can be viewed as a categorical product in a modified category. Unlike in the standard case where the system of basic generators ("simplest objects") is very transparent but necessarily infinite, we have here a single generator. Using just a single generator would lead to increasing complexity value even for structurally very trivial objects just because of the size. Thus, for more satisfactory results,

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... it is advisable to use a transparent infinite system. Such one is proposed and several estimates for the resulting dimension are proved.