Strong and Semi Strong Outer Mod Sum Graphs

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 each vertex v of G, there exist vertices w1, w2 in V (G) such that f(w1) = ∑ u∈N(v) f(u) and f(v) = ∑ u∈N(w2) f(u), 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 Pn for all n = 3, the Cycle C6, and the Complete graphs Kn for all n = 3 are semi strong outer mod sum graphs. Mathematics Subject Classification: 05C78, 05C12, 05C15