Abstract
Functional digraphs are sometimes fractal sets. As a special kind of fractal sets, the dimension properties of the functional digraph are studied in this paper. Firstly, the proof of a Minkowski dimension theorem is discussed and a new proof is given. Secondly, according to this dimension theorem, the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions are discussed. And the relations between these Minkowski dimensions and the Minkowski dimensions of the digraphs of the two functions are established. In the conclusion, the maximum Minkowski dimension of the two functional digraphs plays a decisive part in the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions.
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