On super edge-magic graphs

Abstract

A graph G = (V, E) is said to be super edge-magic if there exists a one-to-one correspondence λ from V ∪ E onto {1, 2, 3,..., |V| + |E|} such that λ(V) = {1,2,..., |V|} and λ(x) + λ(xy) + λ(y) is constant for every edge xy. In this paper, given a positive integer k (k ≥ 6) we use the partitions of k having three distinct parts to construct infinitely many super edge-magic graphs without isolated vertices with edge magic number k. Especially we use this method to find graphs with the maximum number of edges among the super edge-magic graphs with v vertices. In addition, we investigate whether or not some interesting families of graphs are super edge-magic.