Generalized Euler s ??function of graph

Abstract

Let G = (V, E) be a simple connected undirected graph. In this paper, we define generalized Euler's Φ-Function of a graph which is the summation of the Euler's ϕ−function of the degree of the vertices of a graph and it is denoted by Φ (G). It is determined the general form of Euler's Φ-function of some standard graphs. Finally, some important results and properties are studied.