Let G be a ( p , q ) graph. An injective map ƒ: V ( G ) → {±1, ±2,...,± p } is called a pair sum labeling if the induced edge function, ƒ_e: E ( G ) →Z -{0} defined by ƒ _e ( uv )=ƒ( u )+ƒ( v ) is one-one and ƒ_e ( E ( G )) is either of the form {± k ₁, ± k ₂,…, ± k_{q /2}} or {± k ₁, ± k ₂,…, ± k _{( q -1)/2}} { k _{( q +1)/2}} according as q is even or odd. Here we prove that every graph is a subgraph of a connected pair sum graph. Also we investigate the pair sum labeling of some graphs which are obtained from cycles. Finally we enumerate all pair sum graphs of order ≤ 5.