A semi strong outer mod sum labeling of a graph G is an injective mapping f : V (G) → Z + with an additional property that for where both the sums are taken under addition modulo m for some positive integer m. A graph G which admits a semi strong outer mod sum labeling is called a semi strong outer mod sum graph. In this paper we show that the Paths P n for all n = 3, the Cycle C 6 , and the Complete graphs K n for all n = 3 are semi strong outer mod sum graphs. Mathematics Subject Classification: 05C78, 05C12, 05C15