Solution of two-classes of Diophantine equations with 2-quasiperiodic functions (Q1592111)

A set of solutions for the equations \(f(x)\pm f(y)= k\) is described, where \(f\) is a 2-quasiperiodic and strictly monotonous function in \(\mathbb{N}_0\). The results are applied for investigation of a diametrically-threshold function for graphs and of a maximal type of complete bipartite graph. The function \(f(x)\) determined on a set \(D\) is called 2-quasiperiodic in \(D\) if \[ (\exists T)(\forall x\in D): [x+2\in D\Rightarrow f(x+2)= f(x)+ T]. \]