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

S. Arockiaraj (Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu)
P. Mahalakshmi (Department of Mathematics, Kamaraj College of Engineering and Technology Virudhunagar, Tamil Nadu, India)
P. Namasivayam (Department of Mathematics, M.D.T. Hindu College, Tirunelveli, Tamilnadu)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications

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.