Proofs of Non-edge-magic for Several Kinds of Composite Graphs about Kn

For a graph G (p, q) , if there is a one-to-one mapping f from V (G)∪E (G) onto an integer set {1,2,..., p+q}, making any edge uv∈E (G) , there are: f (u)+ f (v)+ f (uv) = k , k is a constant, graph G (p, q) is called edge-magic total labeling graph. Otherwise, it is a non-edge-magic total labeling graph. In this paper, a new algorithm is designed to determine whether the graph is a non-edge magic total labeling graph. Through this algorithm, all non-edge magic total graphs within 9 vertices are obtained. This paper defines a new graph operator ↑ . By introducing the Sidon sequence, it is proved that composite graphs K
n
↑ P
m
, K
n
↑ C
m
, K
n
↑ F
m
are non-edge-magic total labeling graphs when , satisfy certain conditions.