A (n,m) graph G =(V,E) is said to be Cubic Harmonious Graph(CHG) if there exists an injective function f:V(G)→{1,2,3,.........,m 3 +1} such that the induced mapping f * chg : E(G)→ {1 3 ,2 3 ,3 3 ,..........,m 3 } defined by f * chg (uv) = (f(u)+f(v)) mod (m 3 +1) is a bijection. The vertex labels are distinct and edge labels are also distinct as well as cubic. In this paper, focus will be given on the result "cubic harmonious labeling of caterpillar graph and (P n, S m ) graph