Abstract
Suppose G = ( V , E ) be a simple graph with p vertices and q edges. An edge-magic total labeling of G is a bijection f : V ∪ E → {1, 2, …, p + q } where there exists a constant r for every edge x y in G such that f ( x )+ f ( y )+ f ( x y )= r . An edge-magic total labeling f is called a super edge-magic total labeling if for every vertex v ∈ V ( G ) , f ( v )≤ p . The super edge-magic total graph is a graph which admits a super edge-magic total labeling. In this paper, we consider some families of super edge-magic total graph G . We construct several graphs from G by adding some vertices and edges such that the new graphs are also super edge-magic total graphs.
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