Divisor function ????(????) gives the residues of ???? which divide it. A function denoted by ????(????) counts the total possible divisors of ???? and ???? gives the list of co-prime integers to ????. Many graphs had been constructed over these arithmetic functions. Using ????(????) and ????(????), a well known graph named as divisor Euler function graph has been constructed. In this paper, we use divisor function and anti Euler function ????′ . We label the symbol ????????(????) tocount those residues of ???? which are not co-prime to ????. By using these functions, we find a new graph, called divisor anti-Euler function graph (DAEFG), denoted as ????(????(????????(????)). Let ????(????(????????(????)) = (????, ????) be a DAEFG, where ???? = {???????? | ????????/????} and ???? = ????????????????? | gcd ?????????, ????????? ≠ 1?. The objective of this sequel is to introduce and discuss the properties of DAEFG. In this work, we discuss novel classes of proposed graph with its structure using loops, cycles, components of graph, degree of its vertices, components as complete, bipartite, planar, Hamiltonian and Eulerian graphs. Also, we find chromatic number, chromatic index and clique of these graphs.