Odd sum labeling of some subdivision graphs

Abstract

An injective function ƒ : V(G) →{0,1, 2,..., q} is an odd sum labeling if the induced edge labeling ƒ* defined by ƒ*(uv) = ƒ (u) + ƒ(v), for all uvє E(G), is bijective and ƒ*(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 have studied the odd sum property of the subdivision of the triangular snake, quadrilateral snake, slanting ladder, Cp ○ K1, H ○ K1, Cm@Cn, the grid graph Pm x Pn, duplication of a vertex of a path and duplication of a vertex of a cycle.