Odd sum labeling of graphs obtained by duplicating any edge of some graphs

An injective function f : V (G)→{0; 1; 2; : : : ; q} is an odd sum labeling if the induced edgelabeling f* defined by f*(uv) = f(u)+f(v); for all uv (element of) E(G); is bijective and f*(E(G))={1; 3; 5; : : : ; 2q-1}.A graph is said to be an odd sum graph if it admits an odd sum labeling.In this paper we study the odd sum property of graphs obtained by duplicating any edge of somegraphs.