Further Results on Square Sum Graph

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, for every uv ∈ E(G) is injective. In this paper we establish that if G is a square sum graph then G∪Pm is square sum, (Km,n) is square sum if and only if m+n ≤ 5 and W 2 n is square sum if and only if n ≤ 5. We proved that shadow graph and split graph of Pn and K1,n are square sum for every n ∈ N. Also union of paths, the sequential join of some classes of square sum graph, mK1,n for m,n ∈ N and Pn K2(attaching K2 to each vertex of Pn) are some classes of square sum graphs.