In this paper, the authors have consider the graph of Mobius function for zero, G(µ_n⁽⁰⁾). For an integer n≥1, the graph of Mobius function for zero is a graph with vertex set {1, 2, 3, …, n} and an edge, between two vertices a,b if the Mobius function value, µ(ab)=0. The authors have studied the basic results of a graph as the degree of vertex, the adjacency of two vertices and the planarity. First, the authors have calculated the minimum degree and the maximum degree of graph of Mobius function for '0'. The sufficient conditions for two vertices to be adjacent in the graph of Mobius function for '0' based on the divisibility of numbers are discussed and also, proved the necessary and sufficient condition for adjacency of two consecutive vertices in the graph of Mobius function for '0'. At the end, the authors have discussed the planarity of the graph according to the number of vertices of the graph.