Generalized the divisor sum Tk-function of graph

Abstract EN

Let G = (V, E) be a simple connected undirected graph.

In this paper, we define generalized the divisor sum Tk-function of a graph which is the summation of the sum of divisor Ok-function of the degree of the vertices of a graph denoted by Tk(G) = Ʃ vϵV(G) σk(deg(v)) and determine the divisor sum Tk-function of some standard graphs and finally some results are proved.