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

Abstract

Abstract 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 Hi(m, m) and Hi(1) (m, m) and chain of even cycles C4,n, C6,n are E-super arithmetic graceful.