Neutrosophic Graphs of Finite Groups

Let G be a finite multiplicative group with identity e and ( ) N G be the Neutrosophic group with indeterminate I . We denote by   , Ne G I , the Neutrosophic graph of G , ( ) N G and I . In this paper, we study the graph   , Ne G I and its properties. Among the results, it is shown that for any finite multiplicative group G ,   , Ne G I is a connected graph of diameter less than or equal to 2. Moreover, for finite group G , we obtain a formula for enumerating basic Neutrosophic triangles in   , Ne G I . Furthermore, for every finite groups G and G , we show that G G  if and only if ( ) N G ( ) N G  , and if ( ) N G ( ) N G  , then   , Ne G I   , Ne G I    .