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I found that the term "Digraph" was coined in 1955 by Frank Harary in "The number of linear, directed, rooted, and connected graphs", and that it was a term actually suggested by George Pólya as Harary later tells in 1989 in "The Pólya Picture Album—Encounters of a Mathematician"

Now, the problem is that in some places like in this one: Earliest Known Uses of Some of the Words of Mathematics (D) it is said that the term "Directed Graph" was also introduced in that same paper

DIGRAPH was used in 1955 by F. Harary in Transactions of the American Mathematical Society. The term directed graph also occurs there [OED].

But if you check older texts like in the first textbook about graph theory: "Theorie der endlichen und unendlichen Graphen" by Dénes Kőnig published in 1936, the Chapter 7 is called: "Basisprobleme für Gerichtete Graphen" which is translated as: "Basis Problems for Directed Graphs"

So, when did the term "Directed Graph" actually appear?

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