On near felicitous labelings of graphs

A simple graph G is called near felicitous if there exists a 1 ? 1 function f:V(G) → {0, 1, 2, . . . , q ? 1, q + 1} such that the set of induced edge labels f *(uv) = (f(u) + f(v)) (mod q) are all distinct when the addition is taken modulo q with residues 1, 2, 3, . . . , q. It is shown that an even subgraph of a near felicitous graph with an even number of edges contain an even number of odd labeled edges. As a consequence, some families of graphs are shown to be non ? near felicitous.