Mobius Function Graph Mn(G)

The study of graphs on positive integer n as its vertex set from 1 to n, the adjacency of vertices defined using tools of number theoretic functions is interesting and may focus new light on structure of the integers. This paper is concerned on some of the structural properties of the Möbius function graphs from the number theoretic Möbius function. Further we have discussed some basic observations, results concerning |E|, subgraph, perfect matching, completeness, independence number and chromatic number of Möbius function graphs along with new induced proper coloring method.