A (p, q) graph G is said to be square sum, if there exists a bijection f : V(G) → {0,1, 2,...,p — 1} such that the induced function f * : E(G)→ N defined by f * (uv) = (f (u))2 + (f (v))2, ∀ uv ∈ E(G) is injective. In this paper we proved that the planar graphs Plm,n,TBL(n,α,k,β) and higher order level joined planar grid admits square sum labeling. Also the square sum properties of several classes of graphs with many odd cycles are studied.