PRESERVATION OF THE ZK-ANTIMAGIC PROPERTY OF A GRAPH UNDER EDGE ADDITION

A simple connected graph G with vertex set V (G) and edge set E(G) is Z(k)-antimagic if there exists a function f : E(G)-> Z(k)\{0} such that the induced function f(+)(v) = Sigma(uv is an element of E(G)) f(uv) is injective. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k : G is Z(k)-antimagic and k >= 2}. In this paper, we prove that IAM(G) subset of IAM(G '), where G ' is any graph obtained by adding simple edges to G (not equal to a 3-path). Furthermore, if G is disconnected and the added edges do not create a new K-3-component in G ', then IAM(G) C IAM(G ').