The Carmichael Function in Graph Theory

Abstract

One of the most flourishing branches of modern Mathematics is the application of graph theory in graph theory. This work presents innovative graph which is an application of some arithmetical functions and this called the Carmichael Function Graph \lambda(G). Using a new technique in order to calculate the results to be found in this research. Moreover this work considered a new kind of application of some arithmetical functions in graph theory. So for this purpose, many basic properties in graph theory, including finding the characteristics of the independence number, domination number, clique number and  chromatic number of this graph have been calculated.