Structures of Digraphs Arizing from Lambert Type Maps

Abstract

The Well-known function W eW is called Lambert Map. This map has been viewed by many researchers for finding the approximate solutions of exponential function especially in numerical analysis. Later, it has been incorporated in number theory for finding integral solutions of exponential congruences under a fixed modulus. Instead of WeW, we use the function W2 e W and call this function as Discrete Lambert Type Function (DLTF). In this work, we produce graphs using DLTF, and discuss their structures. We show that the digraphs over DLTF satisfy many structures as these have been followed for using WeW. It would be of great interest, if these results could be generalized for WeWfor all integers n, in the future.