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

Abstract E-super arithmetic graceful labelling of a graph G is bijection f from the union vertex set and edge to positive integers (1, 2, 3, … |V(G) ∪ E(G)|) such that edges have labels {1, …, |E(G)|} induced mapping * given by (uv) = f(u) + f(v) − f(uv) for uv ∈ E(G) has range {|V(G) E(G)| 1, |V(G)| 2|E(G)|} In this paper we prove H i (m, m) (1) chain even cycles C 4,n , 6,n are graceful.