The Join Mapping of two Stratified Graphs

Using the mappings u1 and u2 that uniquely define [9] two stratified graphs G1 and G2, respectively, we define the mapping u1 + u2. This mapping is used in further research to define the least upper bound of stratified graphs G1 and G2. The upper bound helps us in future research to prove the closure under union set operation of stratified languages, a family of languages generated by stratified graphs. A few properties, including the associativity of the operation + are proved.