Positive binary labelling of graphs

(V,E) be a finite undirected graph with vertex set V and edge set E. A mapping f ~ {O.l}m is called an M-coding of G, if the induced mapping g : V ~ {O,l • defined as g(v) f(uv). assigns ueV,uveE different vectors to the vertices of G, where all summations are mod 2.An M-coding f is calle~ positive if the zero vector is not assigned to any edge and the induced labelling g does not assign the zero vector to any vertex. Let meG) be the smallest number m for which an M-codlng (positive M-codlng) of G is possible. Trivially, Aigner and Triesch proved that a recent paper, we determined meG). Tuza proved that (G) ~ meG) + 2. In this paper we prove that