E-super arithmetic graceful labelling of H_i(m, m), H_i⁽¹⁾ (m, m) and chain of even cycles

E-super arithmetic graceful labelling of a graph G is a bijection f from the union of the vertex set and edge set to the set of positive integers (1, 2, 3, … |V(G) ∪ E(G)|) such that the edges have the labels from the set {1, 2, 3, …, |E(G)|} and the induced mapping f^* given by f^* (uv) = f(u) + f(v) − f(uv) for uv ∈ E(G) has the range {|V(G) ∪ E(G)| + 1, |V(G) ∪ E(G)| + 2, …, |V(G)| + 2|E(G)|}

In this paper we prove that H_i(m, m) and H_i⁽¹⁾ (m, m) and chain of even cycles C_4,n, C_6,n are E-super arithmetic graceful.