Abstract
An injective function $f:V(G)\rightarrow \{0,1,2,\dots,q\}$ is an odd sum labeling if the induced edge labeling $f^*$ defined by $f^*(uv)=f(u)+f(v),$ for all $uv\in E(G),$ is bijective and $f^*(E(G))=\{1,3,5,\dots,2q-1\}.$ 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 some graphs.
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