Graph easy sets of mute lambda terms

Among the unsolvable terms of the lambda calculus, the mute ones are those having the highest degree of undefinedness. In this paper, we define for each natural number n, an infinite and recursive set Mn of mute terms, and show that it is graph-easy: for any closed term t of the lambda calculus there exists a graph model equating all the terms of Mn to t. Alongside, we provide a brief survey of the notion of undefinedness in the lambda calculus.