Odd Sum Labling of Some Subdivision Graphs

S. Arockiaraj, P. Mahalakshmi, P. Namasivayam

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 have studied the odd sum property of the subdivision of the triangular snake, quadrilateral snake, slanting ladder, $C_pdot K_1$, $Hdot K_1$, $C_m @C_n$, the grid graph $P_mimes P_n$, duplication of a vertex of a path and duplication of a vertex of a cycle.